diff --git a/CHANGELOG.md b/CHANGELOG.md
index 6dab280a5..77d3317bd 100644
--- a/CHANGELOG.md
+++ b/CHANGELOG.md
@@ -22,6 +22,7 @@
 
 ### Fixed
 
+- Keep a layer where it is drawn when it moves into or out of a rotated or flipped parent, instead of shifting it and leaving it at its old angle (#737).
 - Size auto-width text from `.pen` files to its content in CLI exports, instead of a 10000px placeholder that stretched hugging frames in HTML and Storybook output, and keep narrow widths a `.pen` file sets explicitly instead of widening multi-character text.
 - Keep grid layouts, rotation, inner shadows, every shadow of a layer, layer and background blur, flex grow, right-to-left direction, and sections in HTML export, which previously turned grids into columns and dropped the rest.
 - Show what to update instead of a blank window when the browser or system WebView is too old, naming the detected macOS, Safari, Chrome, Edge, Firefox, WebKitGTK, or WebView2 version and linking a prefilled bug report, and explain a failed start the same way (#744).
diff --git a/packages/scene-graph/src/coordinate.ts b/packages/scene-graph/src/coordinate.ts
index c52611d61..c76d1c252 100644
--- a/packages/scene-graph/src/coordinate.ts
+++ b/packages/scene-graph/src/coordinate.ts
@@ -224,3 +224,31 @@ export function getWorldHandles(
     w: { x: pts[14], y: pts[15] }
   }
 }
+
+type LocalTransform = Pick<SceneNode, 'x' | 'y' | 'rotation' | 'flipX' | 'flipY'>
+
+/**
+ * Local transform that draws `node` with the given world matrix once it sits under a parent
+ * whose world matrix is `parentWorld`. Keeps the node's own `flipX` when the matrix allows it.
+ */
+export function localTransformFromWorld(
+  node: SceneNode,
+  world: Mat3,
+  parentWorld: Mat3
+): LocalTransform | null {
+  const parentInverse = Matrix.invert(parentWorld)
+  if (!parentInverse) return null
+  const local = Matrix.multiply(parentInverse, world)
+  const [a, b, , c, d] = local
+  const sx = node.flipX ? -1 : 1
+  const sy = a * d - b * c < 0 ? -sx : sx
+  let rotation = (Math.atan2(sy * c, sx * a) * 180) / Math.PI
+  if (Math.abs(rotation) < 1e-9) rotation = 0
+  const transform = { rotation, flipX: sx < 0, flipY: sy < 0 }
+  const origin = getNodeLocalMatrix({ ...node, ...transform }, { x: 0, y: 0 })
+  return { ...transform, x: local[2] - origin[2], y: local[5] - origin[5] }
+}
+
+export function isTranslationOnly(matrix: Mat3): boolean {
+  return matrix[0] === 1 && matrix[1] === 0 && matrix[3] === 0 && matrix[4] === 1
+}
diff --git a/packages/scene-graph/src/index.ts b/packages/scene-graph/src/index.ts
index 6aee0c87f..91edde7a2 100644
--- a/packages/scene-graph/src/index.ts
+++ b/packages/scene-graph/src/index.ts
@@ -41,6 +41,7 @@ import { cloneNodeProps } from './copy'
 import { bindNodeEvents } from './events'
 import * as HitTest from './hit-test'
 import * as Instances from './instances'
+import Matrix, { type Mat3 } from './matrix'
 import { CONTAINER_TYPES, createDefaultNode } from './node-defaults'
 import { updateNodePreview, type NodePreviewObserver } from './preview'
 import { styleDetachmentChanges } from './shared-styles'
@@ -54,7 +55,13 @@ export * from './types'
 
 import type { Emitter } from 'nanoevents'
 
-import { getAbsolutePosition } from './coordinate'
+import {
+  getAbsolutePosition,
+  getNodeLocalMatrix,
+  getWorldMatrix,
+  isTranslationOnly,
+  localTransformFromWorld
+} from './coordinate'
 import type { Color, Rect, Vector } from './primitives'
 import type {
   DocumentColorSpace,
@@ -507,12 +514,8 @@ export class SceneGraph {
     const oldParentId = node.parentId
     this.absPosCache.clear()
 
-    const absPos = this.getAbsolutePosition(nodeId)
-    const newParentNode = this.nodes.get(newParentId)
-    const newParentAbs =
-      newParentId === this.rootId || newParentNode?.type === 'CANVAS'
-        ? { x: 0, y: 0 }
-        : this.getAbsolutePosition(newParentId)
+    const oldParentWorld = this.parentWorldMatrix(oldParent)
+    const newParentWorld = this.parentWorldMatrix(newParent)
 
     if (oldParent) {
       oldParent.childIds = oldParent.childIds.filter((cid) => cid !== nodeId)
@@ -521,12 +524,23 @@ export class SceneGraph {
     node.parentId = newParentId
     newParent.childIds.push(nodeId)
 
-    node.x = absPos.x - newParentAbs.x
-    node.y = absPos.y - newParentAbs.y
+    if (isTranslationOnly(oldParentWorld) && isTranslationOnly(newParentWorld)) {
+      node.x += oldParentWorld[2] - newParentWorld[2]
+      node.y += oldParentWorld[5] - newParentWorld[5]
+    } else {
+      const world = Matrix.multiply(oldParentWorld, getNodeLocalMatrix(node))
+      const local = localTransformFromWorld(node, world, newParentWorld)
+      if (local) Object.assign(node, local)
+    }
 
     this.emitter.emit('node:reparented', nodeId, oldParentId, newParentId)
   }
 
+  private parentWorldMatrix(parent: SceneNode | undefined): Mat3 {
+    if (!parent || parent.id === this.rootId) return Matrix.identity()
+    return getWorldMatrix(parent, this)
+  }
+
   reorderChild(nodeId: string, parentId: string, insertIndex: number): void {
     const node = this.nodes.get(nodeId)
     if (!node) return
diff --git a/tests/engine/scene-graph/reparent-transform.test.ts b/tests/engine/scene-graph/reparent-transform.test.ts
new file mode 100644
index 000000000..e4c59ff32
--- /dev/null
+++ b/tests/engine/scene-graph/reparent-transform.test.ts
@@ -0,0 +1,109 @@
+import { describe, expect, test } from 'bun:test'
+
+import { getWorldMatrix, SceneGraph, TransformMatrix } from '@open-pencil/scene-graph'
+
+function setup() {
+  const graph = new SceneGraph()
+  const pageId = graph.getPages()[0].id
+  return { graph, pageId }
+}
+
+function worldCorners(graph: SceneGraph, id: string) {
+  const node = graph.getNode(id)
+  if (!node) throw new Error(`missing node ${id}`)
+  const w = node.width
+  const h = node.height
+  return TransformMatrix.mapPoints(getWorldMatrix(node, graph), [0, 0, w, 0, w, h, 0, h])
+}
+
+function expectSameCorners(actual: number[], expected: number[]) {
+  expect(actual).toHaveLength(expected.length)
+  actual.forEach((value, index) => expect(value).toBeCloseTo(expected[index], 6))
+}
+
+describe('reparentNode keeps the node where it is drawn', () => {
+  test('moving into a rotated frame keeps the corners and counter-rotates the node', () => {
+    const { graph, pageId } = setup()
+    const frame = graph.createNode('FRAME', pageId, {
+      x: 100,
+      y: 50,
+      width: 240,
+      height: 240,
+      rotation: 30
+    })
+    const rect = graph.createNode('RECTANGLE', pageId, { x: 500, y: 400, width: 40, height: 20 })
+    const before = worldCorners(graph, rect.id)
+
+    graph.reparentNode(rect.id, frame.id)
+
+    expectSameCorners(worldCorners(graph, rect.id), before)
+    expect(graph.getNode(rect.id)?.rotation).toBeCloseTo(-30, 6)
+  })
+
+  test('moving into a rotated frame and back out restores the original transform', () => {
+    const { graph, pageId } = setup()
+    const frame = graph.createNode('FRAME', pageId, {
+      x: 100,
+      y: 50,
+      width: 240,
+      height: 240,
+      rotation: 30
+    })
+    const rect = graph.createNode('RECTANGLE', pageId, { x: 500, y: 400, width: 40, height: 20 })
+
+    graph.reparentNode(rect.id, frame.id)
+    graph.reparentNode(rect.id, pageId)
+
+    const node = graph.getNode(rect.id)
+    expect(node?.x).toBeCloseTo(500, 6)
+    expect(node?.y).toBeCloseTo(400, 6)
+    expect(node?.rotation).toBeCloseTo(0, 6)
+  })
+
+  test('moving into a flipped frame keeps the corners', () => {
+    const { graph, pageId } = setup()
+    const frame = graph.createNode('FRAME', pageId, {
+      x: 100,
+      y: 100,
+      width: 300,
+      height: 200,
+      flipX: true
+    })
+    const rect = graph.createNode('RECTANGLE', pageId, {
+      x: 150,
+      y: 120,
+      width: 40,
+      height: 20,
+      rotation: 15
+    })
+    const before = worldCorners(graph, rect.id)
+
+    graph.reparentNode(rect.id, frame.id)
+
+    expectSameCorners(worldCorners(graph, rect.id), before)
+    const node = graph.getNode(rect.id)
+    expect(node?.flipX).not.toBe(node?.flipY)
+  })
+
+  test('a rotated node moved between unrotated frames keeps its corners and rotation', () => {
+    const { graph, pageId } = setup()
+    const left = graph.createNode('FRAME', pageId, { x: 0, y: 0, width: 200, height: 200 })
+    const right = graph.createNode('FRAME', pageId, { x: 300, y: 40, width: 200, height: 200 })
+    const rect = graph.createNode('RECTANGLE', left.id, {
+      x: 20,
+      y: 30,
+      width: 60,
+      height: 20,
+      rotation: 45
+    })
+    const before = worldCorners(graph, rect.id)
+
+    graph.reparentNode(rect.id, right.id)
+
+    expectSameCorners(worldCorners(graph, rect.id), before)
+    const node = graph.getNode(rect.id)
+    expect(node?.x).toBe(-280)
+    expect(node?.y).toBe(-10)
+    expect(node?.rotation).toBe(45)
+  })
+})