diff --git a/src/codec-data.ts b/src/codec-data.ts
index 26fa41e..4882752 100644
--- a/src/codec-data.ts
+++ b/src/codec-data.ts
@@ -212,17 +212,6 @@ export const concatNalUnitsInLengthPrefixed = (nalUnits: Uint8Array[], lengthSiz
 	return result;
 };
 
-/** Converts an AVC packet in Annex B format to length-prefixed format. */
-export const transformAnnexBToLengthPrefixed = (packetData: Uint8Array) => {
-	const nalUnits = findNalUnitsInAnnexB(packetData);
-	if (nalUnits.length === 0) {
-		// It's not valid Annex B data
-		return null;
-	}
-
-	return concatNalUnitsInLengthPrefixed(nalUnits, 4);
-};
-
 // Data specified in ISO 14496-15
 export type AvcDecoderConfigurationRecord = {
 	configurationVersion: number;
diff --git a/src/isobmff/isobmff-muxer.ts b/src/isobmff/isobmff-muxer.ts
index e866f9d..fd73b50 100644
--- a/src/isobmff/isobmff-muxer.ts
+++ b/src/isobmff/isobmff-muxer.ts
@@ -25,11 +25,12 @@ import {
 import { BufferTarget } from '../target';
 import { EncodedPacket, PacketType } from '../packet';
 import {
+	concatNalUnitsInLengthPrefixed,
 	extractAvcDecoderConfigurationRecord,
 	extractHevcDecoderConfigurationRecord,
+	findNalUnitsInAnnexB,
 	serializeAvcDecoderConfigurationRecord,
 	serializeHevcDecoderConfigurationRecord,
-	transformAnnexBToLengthPrefixed,
 } from '../codec-data';
 import { buildIsobmffMimeType } from './isobmff-misc';
 import { MAX_BOX_HEADER_SIZE, MIN_BOX_HEADER_SIZE } from './isobmff-reader';
@@ -464,15 +465,18 @@ export class IsobmffMuxer extends Muxer {
 
 			let packetData = packet.data;
 			if (trackData.info.requiresAnnexBTransformation) {
-				const transformedData = transformAnnexBToLengthPrefixed(packetData);
-				if (!transformedData) {
+				const nalUnits = findNalUnitsInAnnexB(packetData);
+				if (nalUnits.length === 0) {
+					// It's not valid Annex B data
 					throw new Error(
 						'Failed to transform packet data. Make sure all packets are provided in Annex B format, as'
 						+ ' specified in ITU-T-REC-H.264 and ITU-T-REC-H.265.',
 					);
 				}
 
-				packetData = transformedData;
+				// We don't strip things like SPS or PPS NALUs here, mainly because they can also appear in the middle
+				// of a stream and potentially modify the parameters of it. So, let's just leave them in to be sure.
+				packetData = concatNalUnitsInLengthPrefixed(nalUnits, 4);
 			}
 
 			const timestamp = this.validateAndNormalizeTimestamp(
diff --git a/test/node/annex-b-conversion.test.ts b/test/node/annex-b-conversion.test.ts
new file mode 100644
index 0000000..3e86555
--- /dev/null
+++ b/test/node/annex-b-conversion.test.ts
@@ -0,0 +1,54 @@
+import { expect, test } from 'vitest';
+import { Input } from '../../src/input.js';
+import { BufferSource, FilePathSource } from '../../src/source.js';
+import path from 'node:path';
+import { ALL_FORMATS } from '../../src/input-format.js';
+import { Output } from '../../src/output.js';
+import { Mp4OutputFormat } from '../../src/output-format.js';
+import { BufferTarget } from '../../src/target.js';
+import { Conversion } from '../../src/conversion.js';
+import { EncodedPacketSink } from '../../src/media-sink.js';
+import { extractAvcNalUnits } from '../../src/codec-data.js';
+
+const __dirname = new URL('.', import.meta.url).pathname;
+
+test('Annex B to length-prefixed conversion, MP4', async () => {
+	using originalInput = new Input({
+		source: new FilePathSource(path.join(__dirname, '..', 'public/annex-b-avc.mkv')),
+		formats: ALL_FORMATS,
+	});
+	const originalVideoTrack = (await originalInput.getPrimaryVideoTrack())!;
+	const originalDecoderConfig = (await originalVideoTrack.getDecoderConfig())!;
+	expect(originalDecoderConfig.description).toBeUndefined();
+	expect(originalVideoTrack.codec).toBe('avc');
+
+	const originalSink = new EncodedPacketSink(originalVideoTrack);
+	const originalFirstPacket = await originalSink.getFirstPacket();
+	expect([...originalFirstPacket!.data.slice(0, 4)]).toEqual([0, 0, 0, 1]);
+
+	const originalNalUnits = extractAvcNalUnits(originalFirstPacket!.data, originalDecoderConfig);
+
+	const output = new Output({
+		format: new Mp4OutputFormat(),
+		target: new BufferTarget(),
+	});
+
+	const conversion = await Conversion.init({ input: originalInput, output });
+	await conversion.execute();
+
+	using newInput = new Input({
+		source: new BufferSource(output.target.buffer!),
+		formats: ALL_FORMATS,
+	});
+	const newVideoTrack = (await newInput.getPrimaryVideoTrack())!;
+	const newDecoderConfig = (await newVideoTrack.getDecoderConfig())!;
+	expect(newDecoderConfig.description).toBeDefined();
+	expect(newVideoTrack.codec).toBe('avc');
+
+	const newSink = new EncodedPacketSink(newVideoTrack);
+	const newFirstPacket = await newSink.getFirstPacket();
+	expect([...newFirstPacket!.data.slice(0, 4)]).not.toEqual([0, 0, 0, 1]); // Successfully converted
+
+	const newNalUnits = extractAvcNalUnits(newFirstPacket!.data, newDecoderConfig);
+	expect(newNalUnits).toEqual(originalNalUnits); // Content is the same though
+});
diff --git a/test/public/annex-b-avc.mkv b/test/public/annex-b-avc.mkv
new file mode 100644
index 0000000..699dfd2
Binary files /dev/null and b/test/public/annex-b-avc.mkv differ