The magnetic properties of small Cr clusters on Fe surfaces have been investigated using a self-consistent noncollinear spd tight-binding method, parametrized through ab initio tight-binding linear muffin-tin orbital results. A competition between antiferromagnetic coupling within the cluster and antiferromagnetic coupling with the Fe surface has been found, leading to noncollinear magnetic arrangements for some configurations. The origin of this behavior is discussed in terms of magnetic frustration and with the aid of Heisenberg exchange parameters, which have been extracted from the calculations.