diff --git a/packages/joint-core/src/V/transform.mjs b/packages/joint-core/src/V/transform.mjs
index ffec7afaed..58f5de7ab3 100644
--- a/packages/joint-core/src/V/transform.mjs
+++ b/packages/joint-core/src/V/transform.mjs
@@ -128,6 +128,16 @@ function getRootSVG(node) {
     return svg;
 }
 
+/**
+ * @param {SVGMatrix} matrix
+ * @returns {boolean}
+ * @description Checks if the given matrix is invertible.
+ */
+function isMatrixInvertible(matrix) {
+    const det = matrix.a * matrix.d - matrix.b * matrix.c;
+    return Number.isFinite(det) && det !== 0;
+}
+
 /**
  *
  * @param {SVGElement} a
@@ -146,7 +156,7 @@ export function getRelativeTransformation(a, b) {
     if (rootA !== rootB) return null;
     // Get the transformation matrix from `a` to `b`.
     const am = b.getScreenCTM();
-    if (!am) return null;
+    if (!am || !isMatrixInvertible(am)) return null;
     const bm = a.getScreenCTM();
     if (!bm) return null;
     return am.inverse().multiply(bm);
diff --git a/packages/joint-core/test/vectorizer/vectorizer.js b/packages/joint-core/test/vectorizer/vectorizer.js
index fee74e8193..5a27df994f 100644
--- a/packages/joint-core/test/vectorizer/vectorizer.js
+++ b/packages/joint-core/test/vectorizer/vectorizer.js
@@ -1648,6 +1648,51 @@ QUnit.module('vectorizer', function(hooks) {
             assert.equal(V.matrixToTransformString(V(svgPath2).getTransformToElement(svgGroup1, { safe: true })), 'matrix(2,0,0,2,20,20)');
         });
 
+        QUnit.test('non-invertible target screen CTM returns identity (no throw)', function(assert) {
+
+            // A scale(0) ancestor produces a singular screen CTM (det = 0)
+            // for descendants. Without the invertibility guard, inverting it
+            // yields a zero/NaN matrix or throws. With the guard,
+            // getRelativeTransformation returns null and getTransformToElement
+            // falls back to identity.
+            var hostGroup = V('g', { transform: 'translate(100, 200)' });
+            var innerPath = V('path', { d: 'M 0 0 L 10 10', transform: 'translate(20, 30)' });
+            hostGroup.append(innerPath);
+            V(svgContainer).append(hostGroup);
+
+            // Baseline: with an invertible ancestor, the source/target
+            // transforms produce a real, non-identity matrix. This proves
+            // the identity result below is the guard's fallback, not a
+            // coincidence of trivial CTMs.
+            var baseline = V(svgCircle).getTransformToElement(innerPath.node);
+            assert.notEqual(
+                V.matrixToTransformString(baseline),
+                'matrix(1,0,0,1,0,0)',
+                'Baseline (invertible ancestor) is not identity'
+            );
+
+            // Collapse the ancestor → target's screen CTM becomes singular.
+            hostGroup.node.setAttribute('transform', 'scale(0)');
+
+            var ctm = innerPath.node.getScreenCTM();
+            assert.ok(ctm, 'Target getScreenCTM returns a matrix');
+            assert.equal(ctm.a, 0, 'Target CTM.a is 0');
+            assert.equal(ctm.b, 0, 'Target CTM.b is 0');
+            assert.equal(ctm.c, 0, 'Target CTM.c is 0');
+            assert.equal(ctm.d, 0, 'Target CTM.d is 0');
+            assert.equal(ctm.a * ctm.d - ctm.b * ctm.c, 0, 'Target CTM determinant is 0');
+
+            // If the call throws, QUnit reports the test as failed.
+            var matrix = V(svgCircle).getTransformToElement(innerPath.node);
+            assert.equal(
+                V.matrixToTransformString(matrix),
+                'matrix(1,0,0,1,0,0)',
+                'Falls back to identity matrix (no throw)'
+            );
+
+            hostGroup.remove();
+        });
+
         QUnit.test('native getTransformToElement vs VElement getTransformToElement - translate', function(assert) {
 
             var container = V(svgContainer);