We address the problem of time optimal software pipelining of loops with control flows, one of the most difficult open problems in the area of parallelizing compilers.We present a necessary condition for loops with control flows to have equivalent time optimal programs, generalizing the result by Schwiegelshohn et al., which has been the most significant theoretical result on the problem. As part of the formal treatment of the problem, we propose a new formalization of software pipelining, which provides a basis of our proof as well as a new theoretical framework for software pipelining research. Being the first generalized result on the problem, our work described in this paper forms an important first step towards time optimal software pipelining.