This paper discusses a static analysis problem, called absolute consistency problem, for relational schema mappings. A given schema mapping is said to be absolutely consistent if every source instance has a corresponding target instance. Absolute consistency is an important property because it guarantees that data exchange never fails for any source instance. Originally, for XML schema mappings, the absolute consistency problem was defined and its complexity was investigated by Amano et al. However, as far as the authors know, there are no known results for relational schema mappings. In this paper, we focus on relational schema mappings such that both the source and the target schemas have functional dependencies, under the assumption that mapping rules are defined by constant-free tuple-generating dependencies. In this setting, we show that the absolute consistency problem is in coNP. We also show that it is solvable in polynomial time if the tuple-generating dependencies are full and the size of the left-hand side of each functional dependency is bounded by some constant. Finally, we show that the absolute consistency problem is coNP-hard even if the source schema has no functional dependency and the target schema has only one; or each of the source and the target schemas has only one functional dependency such that the size of the left-hand side of the functional dependency is at most two.