  We consider the Markovian Master Equation over matrix algebra $\mathbb{M}_d$,
governed by periodic Lindbladian $L_t$ in standard
(Kossakowski-Lindblad-Gorini-Sudarshan) form. It is shown that under
simplifying assumption of commutativity, i.e. if $L_t L_{t'} = L_{t'}L_t$ for
any moments of time $t,t'\in\mathbb{R}_+$, the Floquet normal form of resulting
completely positive dynamical map is not guaranteed to be given by
simultaneously globally Markovian maps. In fact, the periodic part of the
solution is even shown to be necessarily non-Markovian. Two examples in algebra
$\mathbb{M}_2$ are explicitly calculated: a periodically modulated random qubit
dynamics, being a generalization of pure decoherence scheme, and a classically
perturbed two-level system, coupled to reservoir via standard ladder operators.
