This paper deals with a new variant of the Inexact Restoration Method of Fischer and Friedlander (COAP, 46, pp. 333-346, 2010). We propose an algorithm that replaces the monotone line-search performed in the tangent phase (with regard to the penalty function) by a non-monotone one. Con- vergence to feasible points satisfying the approximate gradient projection (AGP) condition is proved under mild assumptions. Numerical results on representative test problems validate and show that the proposed ap- proach outperforms the monotone version when a suitable non-monotone parameter is chosen.