In 2004, Sekhar proposed a new signature scheme with message recovery. Based on this signature scheme with message recovery, they also proposed a designated verifier signature scheme with non-repudiation of origin and a convertible designated verifier signature scheme with non-repudiation of origin. This paper, however, presents a security analysis where Sekhar's signature schemes are vulnerable to some forgery attacks. This means that any attacker can forge a signature for any message.