We study the occurrence of ground-state factorization in dimerized $XY$ spinchains in a transverse field. Together with the usual ferromagnetic andantiferromagnetic regimes, a third case emerges, with no analogous intranslationally-invariant systems, consisting of an antiferromagneticNe\'{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 thefactorizing field represent an accidental degeneracy point of the Hamiltonian.Finally, we extend the study of the existence of ground-state factorization toa more general class of models.
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