Recently, Kim et al.'s proposed a new type of proxy signature scheme, called self proxy signature scheme. In their scheme, a signer, delegates his/her signing capability to himself/herself and uses the proxy private/public key pair as temporary keys. In this paper, we will demonstrate some security leaks inherent in Kim et al.'s scheme and show that an adversary can forge a valid self proxy sig- nature for any message by using different ways. Finally, we will propose an improvement to eliminate the pointed out security leaks.