Multivariate Public Key Cryptosystems (MPKC) is one of candidates for post-quantum cryptography. Rainbow is an MPKC digital signature scheme, with relatively efficient encryption and decryption processes. However, the size of MPKC key is substantially larger than that of an RSA cryptosystem for the same security level. In this paper, we propose a variant of Rainbow that has a smaller secret key. The smaller secret key is to the result of a different description of the quadratic polynomials appearing in the secret key from that of the original Rainbow. In addition, our scheme improves the efficiency of the Rainbow’s signature generation. In particular, the secret key is reduced in size by about 40% and the signature generation is sped up by about 30% at the security level of 100 bits.