Radiative corrections to the masses M of the vector bosons W and Z increase in perturbation theory with increasing Higgs mass m. Since these masses will be experimentally determined to an accuracy on the order of 0.1%, these measurements may offer one of the best tests of the detailed dynamics of the standard model. In particular, they would seem to place an upper limit on the Higgs mass rn (or, since rn 2 ~ h, the maximum strength of the scalar self-coupling k). Performing a 1IN expansion in

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... (N) X U(1) through order 1IN but all orders in the scalar coupling kN, it is demonstrated that the radiative corrections 8M 2 to the vector boson masses are of the form ~M 2/M 2 = (,g2N/167r 2 ) [F t (0 w) + N -I F 2 (kN, 0 w) + O(N-2)], where g2N is the SU(N) gauge coupling constant and 0 w the weak mixing angle. The function F 2 remains finite even in the limit of infinite self-coupling constant. Thus, no matter how large the perturbative Higgs mass m is, the vector boson mass shifts may remain small, on the order of the anticipated experimental accuracy.