A major difficulty concerning test data generation for white box testing is to detect the domain of input variables covering a certain path. With this aim, a new concept, domain coverage, is introduced in this article. In search of appropriate input variable subdomains, covering a desired path, the domains are randomly partitioned as far as subdomains whose boundaries satisfy the path constraints are found. When partitioning, the priority is given to those subdomains whose boundary variables do not satisfy the path constraints. Representing the relation between the subdomains and their parents as a directed acyclic graph, an Euler/Venn reasoning system could be applied to select the most appropriate subdomains. To evaluate our proposed path oriented test data generation method, the results of applying the method to six known benchmark programs, triangle, GCD, calday, shellsort, quicksort and heapsort, is presented.