  A single-electron transistor (SET) in a magnetic field irradiated with
microwaves is studied theoretically in non-equilibrium Kondo regime. The two
fold effect of frequency--\Omega--microwaves is considered as follows: the
oscillations in the voltage with frequency \Omega and in the coupling
parameters with frequency \Omega/p (p\in\mathbb{N}). We describe the system by
the Kondo model at a specific point in the Toulouse limit. A non-perturbative
technique is proposed, namely, the non-equilibrium Green's functions and
physical observables are averaged over a period of 2\pi p/\Omega. When the
microwave irradiation is considered affecting only the voltage, one sees the
Kondo satellites as stated in the previous studies. Moreover, the features of
the differential conductance and magnetic susceptibility of a SET become richer
when the Kondo couplings are considered oscillating on time. We obtain the
satellite peak splitting. It explains the possibilities one can find in
experimental results that the distance between peaks, which appear in the
differential conductance -- magnetic amplitude characteristics G(H) or in the
differential conductance -- dc voltage characteristics G(V_{dc}), can be
smaller than \hbar\Omega.
