In this paper, we discuss the collision search for hash functions, mainly in terms of their advanced message modification. The advanced message modification is a collision search tool based on Wang et al.'s attacks. Two advanced message modifications have previously been proposed: cancel modification for MD4 and MD5, and propagation modification for SHA-0. In this paper, we propose a new concept of advanced message modification, submarine modification. As a concrete example combining the ideas underlying these modifications, we apply submarine modification to the collision search for SHA-0. As a result, we show that this can reduce the collision search attack complexity from 2³⁹ to 2³⁶ SHA-0 compression operations.