This paper studies the generalization of Zinder-Roper algorithm for maximum lateness problem to the case of dedicated processors systems with constant delays. One of remarkable feature of this algorithm is that it is based on iterated list scheduling, without any other computation. The performance of the extended algorithm is evaluated through worst-case analysis. If all tasks have the same type and no delay is considered, then the upper bound obtained coincides with the upper bound for Zinder-Roper algorithm on identical processors, which is the best known for maximum lateness problem.