Many researchers have compared the fault-detecting ability of random testing and partition testing with test cases replacement. Great achievements have been gained. Comparing random testing with partition testing without test cases replacement has not been found in existing documents. However, in practice, especially at the early stage of testing and during module testing, test cases are not replaced. Therefore, it is necessary to compare random with partition testing under this case. In this paper it is done and four findings are proposed. One difference from the results done by Chen and Yu is that when the domain is divided into such subdomains with the same size, the same failures and same test numbers, partition testing performed worst than random testing. How to form a subdomain with heavy failures by use of all kinds of information and then gives it a large number of tests is essential for partition testing.