  We consider a model Venttsel type problem for linear parabolic systems of
equations. The Venttsel type boundary condition is fixed on the flat part of
the lateral surface of a given cylinder. It is defined by parabolic operator
(with respect to the tangential derivatives) and the conormal derivative. The
H\"{o}lder continuity of a weak solution of the problem is proved under optimal
assumptions on the data. In particular, only boundedness in the time variable
of the principal matrices of the system and the boundary operator is assumed.
All results are obtained by so-called A(t)-caloric method.
