The author establishes a computational procedure for finding the order of a pole of the inverse of any \(n\times n\) meromorphic matrix function \(A( z) =\sum_{j=-\nu}^{\infty}( z-z_{0}) ^{j}A_{j},\) where \(A_{j}\in \mathbb{C}^{n\times n},\) \(A_{-\nu}\neq 0.\) A vector-valued function \(\Phi( z) \) such that \(\Phi( z) \) is analytic at \(z_{0},\) \(\Phi( z_{0}) \neq 0,\) \(A( z) \Phi( z) \) is analytic at \(z_{0},\) and \(A( z) \Phi( z) _{|z=z_{0}}=0,\) is called a null function of \(A( z) .\) The order of \(z_{0}\) as a zero of \(A( z) \Phi( z) \) is called the order of the full function \(\Phi( z) \) of \(A^{-1}( z) =\sum_{j=-s}^{\infty}( z-z_{0}) ^{j}B_{j}\) with \(B_{s}\neq 0.\) The author gives the answer to the question what is the number \(s\).