diff --git a/packages/@aws-cdk/aws-lambda-nodejs/lib/util.ts b/packages/@aws-cdk/aws-lambda-nodejs/lib/util.ts
index 6b3f7f8173a02..9bdab8776c86c 100644
--- a/packages/@aws-cdk/aws-lambda-nodejs/lib/util.ts
+++ b/packages/@aws-cdk/aws-lambda-nodejs/lib/util.ts
@@ -54,12 +54,16 @@ export function nodeMajorVersion(): number {
  * Find a file by walking up parent directories
  */
 export function findUp(name: string, directory: string = process.cwd()): string | undefined {
-  const { root } = path.parse(directory);
-  if (directory === root && !fs.existsSync(path.join(directory, name))) {
-    return undefined;
-  }
+  const absoluteDirectory = path.resolve(directory);
+
   if (fs.existsSync(path.join(directory, name))) {
     return directory;
   }
-  return findUp(name, path.dirname(directory));
+
+  const { root } = path.parse(absoluteDirectory);
+  if (absoluteDirectory === root) {
+    return undefined;
+  }
+
+  return findUp(name, path.dirname(absoluteDirectory));
 }
diff --git a/packages/@aws-cdk/aws-lambda-nodejs/test/util.test.ts b/packages/@aws-cdk/aws-lambda-nodejs/test/util.test.ts
index 026f2bcb519e3..a85b0064cef85 100644
--- a/packages/@aws-cdk/aws-lambda-nodejs/test/util.test.ts
+++ b/packages/@aws-cdk/aws-lambda-nodejs/test/util.test.ts
@@ -10,4 +10,10 @@ test('findUp', () => {
 
   // Starting at a specific path
   expect(findUp('util.test.ts', path.join(__dirname, 'integ-handlers'))).toMatch(/aws-lambda-nodejs\/test$/);
+
+  // Non existing file starting at a non existing relative path
+  expect(findUp('not-to-be-found.txt', 'non-existing/relative/path')).toBe(undefined);
+
+  // Starting at a relative path
+  expect(findUp('util.test.ts', 'test/integ-handlers')).toMatch(/aws-lambda-nodejs\/test$/);
 });