This paper deals with the Cauchy-Dirichlet problem for second-order quasilinear parabolic operators in non-divergence form with discontinuous data. The authors consider its formal linearization obtained by derivation in the Fréchet sense at some fixed solution \( u_{0} \in W_{p}^{2,1} \), \( p > n+2 \), of the above mentioned Cauchy-Dirichlet problem. This way they obtain a linear non-degenerate problem. Applying the implicit function theorem, it is shown that for all small \( L^{\infty} \)-perturbations of the data there exists, locally in time, one and only one solution \( u \) of the perturbed problem which is close to \( u_{0} \) in \( W_{p}^{2,1} \) and depends smoothly on the data (Theorem 4). In Theorem 5, an approximating sequence for \( u_{0} \) is constructed via the Newton iteration procedure.