In the spectral and scattering theory for a Schr\"odinger operator with a time-periodic potential $H(t)=p^2/2+V(t,x)$, the Floquet Hamiltonian $K=-i\partial_t+H(t)$ associated with $H(t)$ plays an important role frequently, by virtue of the Howland-Yajima method. In this paper, we introduce a new conjugate operator for $K$ in the standard Mourre theory, that is different from the one due to Yokoyama, in order to relax a certain smoothness condition on $V$.