  A structure is called homogeneous if every isomorphism between finite
substructures of the structure extends to an automorphism of the structure.
Recently, P. J. Cameron and J. Ne\v{s}et\v{r}il introduced a relaxed version of
homogeneity: we say that a structure is homomorphism-homogeneous if every
homomorphism between finite substructures of the structure extends to an
endomorphism of the structure. In this paper we characterize all finite
homomorphism-homogeneous relational systems with one irreflexive binary
relation.
