diff --git a/packages/core/src/index.ts b/packages/core/src/index.ts
index d20e964b..f9a4463c 100644
--- a/packages/core/src/index.ts
+++ b/packages/core/src/index.ts
@@ -108,7 +108,7 @@ export abstract class SDJwtInstance<ExtendedPayload extends SdJwtPayload> {
       header,
       payload: {
         ...packedClaims,
-        _sd_alg: hashAlg,
+        _sd_alg: disclosureFrame ? hashAlg : undefined,
       },
     });
     await this.SignJwt(jwt);