In this paper we consider the singular, finite horizon, state feedback H-infinity control problem for linear time-varying systems. Singular problem means that the feedthrough matrix between the control input and the controlled output is not full column rank; in this case we prove that the original H-infinity problem is equivalent to another H-infinity problem related to a reduced order system. If this problem is regular it can be solved via standard techniques, conversely we can iterate the reduction procedure. We show that this iterative procedure terminates when either a trivial problem is encountered or the last reduced order problem is nonsingular.