Recently Lee-Chang proposed a new strong designated verifier signature scheme. They claimed that their proposed scheme is more secure and suitable for the purpose of a strong designated verifier signature scheme. This paper shows that Lee-Chang scheme cannot withstand forgery attack which an adversary can forge a signature without knowing the secret key of the signer or the designated verifier and an improved scheme is presented to overcome the security weaknesses of their scheme. The security of the scheme is enhanced by adding the secret key of the signer in signature generation phase. The analysis shows that the new scheme resolves security problems in the previous scheme, meets the aspects of security feathers needed by strong designated verifier signature scheme.