In open quantum system study, it is commonly accepted notion that Markovian dynamic, which does not depend on past history, exhibits a completely positive (CP) divisible dynamical map while non-Markovian one, depending on the entire past history, evolves under non-CP divisible dynamical map. In this talk, we provide a general description of a time-local master equation for a system coupled to a non-Markovian reservoir based on the Floquet theory. This allows us to have a divisible dynamical map at discrete times, which we refer to as Floquet stroboscopic divisibility (FSD). We illustrate the theory by considering a quantum harmonic oscillator coupled to both non-Markovian and Markovian baths. Our findings provide us with a theory for the exact calculation of spectral properties of time-local non-Markovian Liouvillian operators. If time permits, application of FSD to dynamical quantum phase transition will be highlighted.