In this paper, we present a restricted tabu search(RTS) algorithm that schedules jobs on identical parallel machines in order to minimize the maximum lateness of jobs. Jobs have release times and due dates. Also, sequence-dependent setup times exist between jobs. The RTS algorithm consists of two main parts. The first part is the MATCS(Modified Apparent Tardiness Cost with Setups) rule that provides an efficient initial schedule for the RTS. The second part is a search heuristic that employs a restricted neighborhood generation scheme with the elimination of non-efficient job moves in finding the best neighborhood schedule. The search heuristic reduces the tabu search effort greatly while obtaining the final schedules of good quality. The experimental results show that the proposed algorithm gives better solutions quickly than the existing heuristic algorithms such as the RHP(Rolling Horizon Procedure) heuristic, the basic tabu search, and simulated annealing.