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In this paper we describe an extension of timed automata with priorities, and efficient algorithms to compute subtraction on DBMs (difference bounded matrices), needed in symbolic model-checking of timed automata with priorities. The subtraction is one of the few operations on DBMs that result in a non-convex set needing sets of DBMs for representation. Our subtraction algorithms are efficient in the sense that the number of generated DBMs is significantly reduced compared to a naive algorithm. The overhead in time is compensated by the gain from reducing the number of resulting DBMs since this number affects the performance of symbolic model-checking. The uses of the DBM subtraction operation extend beyond timed automata with priorities. It is also useful for allowing guards on transitions with urgent actions, deadlock checking, and timed games.