diff --git a/src/languageFeatures/fileRename.ts b/src/languageFeatures/fileRename.ts
index 5c727e3..6094f1c 100644
--- a/src/languageFeatures/fileRename.ts
+++ b/src/languageFeatures/fileRename.ts
@@ -172,6 +172,11 @@ export class MdFileRenameProvider extends Disposable {
 		if (link.href.kind !== HrefKind.Internal) {
 			return false;
 		}
+		
+		if (link.source.hrefText.startsWith('#')) {
+			// No rewrite needed as we are referencing the current doc implicitly
+			return false;
+		}
 
 		if (link.source.hrefText.startsWith('/')) {
 			// We likely don't need to update anything since an absolute path is used
diff --git a/src/test/fileRename.test.ts b/src/test/fileRename.test.ts
index 402b5b4..2545b93 100644
--- a/src/test/fileRename.test.ts
+++ b/src/test/fileRename.test.ts
@@ -490,6 +490,9 @@ suite('File Rename', () => {
 			`[abc](../old)`,
 			`[abc](/old)`,
 			`[abc](/old/)`,
+			``, // Own header links should not get rewritten here
+			`# header`,
+			`[text](#header)`,
 		));
 
 		const workspace = store.add(new InMemoryWorkspace([
@@ -516,4 +519,38 @@ suite('File Rename', () => {
 			]
 		});
 	}));
+
+	test('Should not rewrite fragment links to self', withStore(async (store) => {
+		// Create workspace state after the rename
+		const newDocUri = workspacePath('sub', 'newReadme.md');
+		const newDoc = new InMemoryDocument(newDocUri, joinLines(
+			`# Header`,
+			`[abc](#header)`, // No change
+			`[abc](oldReadme.md#header)`, // Needs rewrite
+			`[abc](./oldReadme.md#header)`, // Needs rewrite
+			``,
+			`[def1]: #header`, // No change
+			`[def2]: oldReadme.md#header`, // Needs rewrite
+			`[def3]: ./oldReadme.md#header`, // Needs rewrite
+		));
+
+		const workspace = store.add(new InMemoryWorkspace([
+			newDoc,
+		]));
+
+		const response = await getFileRenameEdits(store, [
+			{ oldUri: workspacePath('oldReadme.md'), newUri: newDocUri },
+		], workspace);
+
+		assertEditsEqual(response!.edit, {
+			// Here we need to be using the new path to 'doc'
+			uri: newDocUri, edits: [
+				lsp.TextEdit.replace(makeRange(2, 6, 2, 18), 'newReadme.md'),
+				lsp.TextEdit.replace(makeRange(3, 6, 3, 20), './newReadme.md'),
+
+				lsp.TextEdit.replace(makeRange(6, 8, 6, 20), 'newReadme.md'),
+				lsp.TextEdit.replace(makeRange(7, 8, 7, 22), './newReadme.md'),
+			]
+		});
+	}));
 });
\ No newline at end of file