As recently been emphasized by NSA and NIST, there is an increasing need for cryptographic schemes being secure against quantum computer attacks. Especially in the area of digital signature schemes,multivariate cryptography is one of the main candidates for this. At Inscrypt 2015, Nie et al. proposed a new multivariate signature scheme called CUOV , whose public key consists both of quadratic and cubic polynomials. However, the scheme was broken by an attack of Hashimoto . In this paper we take a closer look on the CUOV scheme and its attack and propose two new multivariate signature schemes called CSSv and SVSv, which are secure against Hashimoto’s attack and all other known attacks on multivariate schemes. Especially our second construction SVSv is very efficient and outperforms current multivariate signature schemes such as UOV and Rainbow in terms of key and signature size.