A method for the computation of the transfer function for linear time-invariant singular SISO systems is presented. The system must be reduced to the Hessen-berg/triangular form, then the transfer function denominator and numerator are obtained by two simple formulae derived from the expression of the determinant of a Hessenberg matrix. The problem of computing a minimal representation by removing the input and output decoupling zeros via Hessenberg/triangular form is also considered. Unitary transformations are used and so the numerical stability is preserved. An extension to multivariable systems is proposed.