In a distributed system, a deadlock may occur when set of processes wait for resources from each other. A process involved in a deadlock waits indefinitely unless a special action is taken. Deadlock leaves the system into a blocking state with no process getting complete and also it reduces the throughput. In this paper a technique is presented that will improve the performance of Srinivasan distributed deadlock algorithm for multiple executions. In Srinivasan algorithm whenever multiple initiators invoke the algorithm one after the other same deadlock cycle and similar message transfers may be reported in more than one execution. So, in order to handle multiple executions an algorithm has been proposed which will not only reduce the number of message transfers but will also reduce the deadlock detection time. The proposed algorithm gives priority to different algorithm execution depending on their process id"s along with this it allows lower priority executions to continue so that a deadlock that are not directly reachable from the higher priority execution could be detected.