Employing 1-bit quantization in massive multiple-input-multiple-output (MIMO) systems is a promising approach to improve the power efficiency. Various linear and nonlinear precoding techniques including the maximum safety margin (MSM) precoder have been presented to cope with severe 1-bit quantization distortions. In this paper, we show the reason for MSM precoder’s success in reducing the quantization distortions and propose a low complexity extension with a greedy algorithm by exploiting this analytic result. Numerical results illustrate that the extended MSM is almost optimal in terms of maximizing the constructive interference (CI) between the received signals.