  We study the occurrence of ground-state factorization in dimerized $XY$ spin
chains in a transverse field. Together with the usual ferromagnetic and
antiferromagnetic regimes, a third case emerges, with no analogous in
translationally-invariant systems, consisting of an antiferromagnetic
Ne\'{e}l-type ground state where pairs of spins represent the unitary cell.
Then, we calculate the exact solution of the model and show that the
factorizing field represent an accidental degeneracy point of the Hamiltonian.
Finally, we extend the study of the existence of ground-state factorization to
a more general class of models.
