This paper describes the necessity, the algorithm, how it works and the performance of a novel model of hand-off for heterogeneous networks that is different from the methods used in the traditional homogeneous networks. The heterogeneous networks are networks that combine two or more technologically different networks. The necessity of a new hand-off method comes with the 4G networks where the traditional methods are not enough to obtain a good performance. For that reason, the designed algorithm measures the quality of service and is named MQoS (Measure of QoS). We did simulations of heterogeneous network that combine UMTS and Wi-Fi networks with the simulation tool J-sim and using our algorithm and we compared the result of them with simulations of hand-off algorithms based in the Received Signal Strength Indicator RSSI. The RSSI is a parameter that is traditionally used by homogeneous networks.