If A is a ω-periodic matrix Floquet's theorem states that the differential equation y′ = Ay has a fundamental matrix P(x) exp(Jx) where J is constant and P is ω-periodic, i.e., P(x) = P*(e2πix=ω). We prove here that P* is rational if A is bounded at the ends of the period strip and if all solutions of y′ = Ay are meromorphic. This version of Floquet's theorem is important in the study of certain integrable systems.