Retiming is a technique to resynthesize a synchronous sequential circuit by rearranging flip-flops. In view of logic optimization, retiming can potentially derive a circuit which is more simplified and testable because retiming can convert several sequential redundancies into combinational redundancies. Retiming methods proposed before have no guarantee to generate the same output sequences when the circuit start from a specified initial state such as the reset state. If the circuit with a specified initial state must have the same output sequences after retiming, rearrangement of flip-flops should be restricted. This paper presents a retiming method for circuits with a specified initial state so that retimed circuits give the same output sequences of the original circuits for any input sequences. In the proposed method, during the procedure of retiming each flip-flop keeps a value corresponding to the initial state and unification of flip-flops with different value is avoided. Our procedure uses 5-valued logic on gate level implementation to describe and calculate the values of flip-flops. Therefore after optimization using our method, the circuit has completely the same behavior as that of the original. Experimental results for ISCAS'89 benchmark circuits show the method can be used to optimize the circuits as well as a method without considering the initial state. And testability of the retimed circuit is more enhanced than that of the original circuit.