The Wyner-Ziv Problem for general sources with average distortion under fixed-length coding is investigated in this paper. To solve the problem, an enhanced covering lemma for a Markov chain is first established. Then based on the lemma, a general formula for the rate-distortion function of the problem is derived, where the distortion is only assumed uniformly bounded and may be nonadditive. Finally, it is further pointed out that such methods can be used to establish more general results on multiterminal source coding problems.