In this paper, a hash function with lower rate but higher efficiency is proposed and it can be built oninsecure compression functions. The security of this scheme is proved under black-box model and somecompression function based on block ciphers are given to build this scheme. It is also shown that key schedule is amore important factor affecting the efficiency of a block-cipher-based hash function than rate. The new schemeonly needs 2 keys and the key schedule of it can be pre-computed. It means the new scheme need not re-schedulethe keys at every step during the iterations and its efficiency is improved.