AbstractWe prove a modification of the so-called A(t)-caloric lemma stated in our earlier work with O. John [1] to study regularity of weak solutions to parabolic systems of non-divergence type with non-smooth in time principal matrices. As an application, we prove smoothness results in Morrey
and Campanato spaces for linear parabolic systems of non-divergence type by the A(t)-caloric
approximation method.