Square root of a matrix play an important role in many applications of matrix theory. In this paper, we propose a new iterative method for square root of a non-singular M-matrix. We first transform the matrix equation X2 β A=0 into special form of a non-symmetric algebraic Riccati equation (NARE), and then solve this special NARE by Newton method. Efficiency and effectiveness proved by theoretical analysis and numerical experiments. Keywords: - Matrix square root, M-matrix, Non-symmetric algebraic Riccati equation, Newton method
