In 2004, a new attack against SHA-1 has been proposed by a team leaded by Wang [15]. The aim of this article is to sophisticate and improve Wang’s attack by using algebraic techniques. We introduce new notions, namely semi-neutral bit and adjuster and propose then an improved message modification technique based on algebraic techniques. In the case of the 58-round SHA-1, the experimental complexity of our improved attack is $2^{31}$ SHA-1 computations, whereas Wang’s method needs $2^{34}$ SHA-1 computations. We have found many new collisions for the 58-round SHA-1. We also study the complexity of our attack for the full SHA-1.