Nonsingular $H$-matrix plays a significant role in the control theory, the scientific computation and the applications in engineering. However, it is difficult to specify a non-singular $H$-matrix in practice. In this paper, we partition the row index set by studying the elements of a matrix, and construct a positive diagonal matrix. Then, we apply some techniques in inequalities to obtain a new criterion for nonsingular $H$-matrices. We also obtain several similar results in the cases of irreducible matrices and matrices with non-zero elements chains. These consequences improve and generalize the related results, and the advantage of the proposed consequences are illustrated by several numerical examples.