The BeppoSAX Gamma Ray Burst Monitor (GRBM) is triggered any time a statistically significant counting excess is simultaneously revealed by at least two of its four independent detectors. Several spurious effects, including highly ionizing particles crossing two detectors, are recorded as onboard triggers. In fact, a large number of false triggers is detected, on the order of 10/day. A software code, based on an heuristic algorithm, was written to discriminate between real and false triggers. We present the results of the analysis on an homogeneous sample of GRBM triggers, thus providing an estimate of the efficiency of the GRB detection system consisting of the GRBM and the software.