A real square matrix whose non-diagonal elements are non-positive is called a Z-matrix. This paper shows a necessary and sufficient condition for non-singularity of two types of Z-matrices. The first is for the Z-matrix whose row sums are all non-negative. The non-singularity condition for this matrix is that at least one positive row sum exists in any principal submatrix of the matrix. The second is for the Z-matrix $\"\"$ which satisfies $\"\"$ where $\"\"$ . Let $\"\"$ be the ith row and the jth column element of $\"\"$ , and $\"\"$ be the jth element of $\"\"$ . Let $\"\"$ be a subset of $\"\"$ which is not empty, and $\"\"$ be the complement of $\"\"$ if $\"\"$ is a proper subset. The non-singularity condition for this matrix is $\"\"$ such that $\"\"$ or $\"\"$ such that $\"\"$ for $\"\"$ . Robert Beauwens and Michael Neumann previously presented conditions similar to these conditions. In this paper, we present a different proof and show that these conditions can be also derived from theirs.