The Alfvén ion cyclotron (AIC) instability margin in a mirror trap with skew injection of fast neutral beams into a target plasma is investigated in the present work. The instability is driven by inverse population of trajectories of resonant ions having velocity near the injection velocity. So, the stability margin depends strongly on injection details, in particular an injection angle and angular width. The absolute instability margin analysis as well as WKB-analysis on longitudinal and transversal coordinates are used for the stability threshold studying. Simple estimations relating the wave parameters to injection parameters are presented. The stabilizing effect of strong transversal non-uniformity is shown.