Horizontally convex polyominoes are finite discrete sets of simply connected elementary cells, such that all of their rows are connected. The problem is to find the best matching between two horizontally convex polyominoes. So, we look for a position of the second polyomino relative to the first one, called a translation, such that the overlapping surface of the two polyominoes is maximal. In this paper, we present an optimal algorithm computing the overlapping surface for all possible translations. Then, we can exhibit the maximal superposition and the related translations.