With the ever evolving mobile communication technology, achieving a high quality seamless mobility access across mobile networks is the present challenge to research and development engineers. Existing algorithms are used to make handover while a mobile station is roaming between cells. Such algorithms have some handover instability due to method of making handover decision. This paper proposes an enhanced handover algorithm that substantially reduces the handover redundancy in vertical and horizontal handovers. Also, it enables users to select the most appropriate target network technology based on their preferences even in the worst case where the mobile station roams between cell boundaries, and has high ability to have efficient performance in the critical area full of interferences. The proposed algorithm uses additional quality of service criteria, such as cost, delay, available bandwidth and network condition with two handover thresholds to achieve a better seamless handover process. After developing and testing this algorithm, the simulation results show a major reduction in the redundant handover, so high accuracy of horizontal and vertical handovers obtained. Moreover, the signal strength is kept at a level higher than the threshold during the whole simulation period, while maintaining low delay and connection cost compared to other two algorithms in both scenarios.