This technical note addresses the computation of the H-infinity norm by directly computing the isolated common zeros of two bivariate polynomials, unlike the iteration algorithm that is currently used to find the H-infinity norm. The proposed method to H-infinity norm calculation is compared with the existing method [by Bruinsma and Steinbuch (1990)] using numerical experiments on random transfer functions of orders upto 240; the time taken is better by 15 to 30 times, in addition to improved accuracy. The proposed method uses techniques involving structured linearization of the Bezoutian matrix constructed from two bivariate polynomials.