The dynamic taint analysis mechanism is used to protect sensitive data in the Android system. But this technique does not detect control flows which can cause an under-tainting problem. This means that some values should be marked as tainted, but are not. The under-tainting problem can be the cause of a failure to detect a leak of sensitive information. To solve this problem, we use a set of formally defined rules that describes the taint propagation. We prove the completeness of these rules. Also, we provide a correct and complete algorithm based on these rules to solve the under-tainting problem.