The job shop scheduling problem with the makespan criterion is a certain NP-hard case from OR theory having excellent practical applications. This problem, having been examined for years, is also regarded as an indicator of the quality of advanced scheduling algorithms. In this paper we provide a new approximate algorithm that is based on the big valley phenomenon, and uses some elements of so-called path relinking technique as well as new theoretical properties of neighbourhoods. The proposed algorithm owns, unprecedented up to now, accuracy, obtainable in a quick time on a PC, which has been confirmed after wide computer tests.