This paper addresses the problem of finding a feasible solution for the University Course Timetabling Problem (UCTP), i.e. a solution that satisfies all the so-called hard constraints. The problem is reformulated through relaxing one of its hard constraints and then creating a soft constraint to address the relaxed constraint. The relaxed problem is solved in two steps. First, a graph-based heuristic is used to construct a feasible solution of the relaxed problem, and then, a Simulated Annealing (SA)-based approach is utilized to minimize the violation of the soft constraint. In order to strengthen the diversification ability of the method in the SA phase, a heuristic based on Kempe Chain neighborhood is embedded into the standard approach. This strategy is tested on a well-known data set, and the results are very competitive compared to the current state of the art of the UCTP.