This paper discusses a new method for eliminating crucial faults in embedded software. Recent embedded software systems contain various functions or provide various services. Reflecting functional explosion of embedded software, the size and complexity of software increases so much. It is difficult to ensure their quality and to eliminate crucial faults by conventional software testing method because, in such large and complex software, too many test cases are required in order to cover all functions in a specification. In this paper, we newly introduce an idea of functional priority testing and develop a new selective testing method. In this method, with prioritizing the functions in the target software, test items are selected according to their functional priorities. Important functions with high priorities are tested in detail, and functions with low priorities are tested less intensively. With using functional priorities, effective testing will be performed. The effectiveness of selective testing will be evaluated during experiments in actual software testing.