The problem of balancing the state space system matrices of a linear time-invariant system prior to computation of its transmission zeros is considered. It is shown that in some cases balancing has a significant effect on the accuracy of the computed transmission zeros. An algorithm designed specifically for balancing the system matrices for the computation of transmission zeros is presented. The paper also presents a new numerically stable algorithm for computation of zeros and gains of transfer functions. Several examples are provided to illustrate the algorithms in the paper.