We consider the Cauchy-Dirichlet problem for second order quasilinear non-divergence form parabolic equations with discontinuous data in a bounded cylinder- Supposing existence of strong solution and applying the Implicit Function Theorem we show that for any small perturbation of the coefficients and the data there exists, locally in time, exactly one solution close to the fixed solution. with respect to the considered norm which depends smoothly on the data. For that, no structure and growth conditions on the data are needed. Moreover, applying the Newton Iteration Procedure we obtain an approximating sequence for the fixed solution.