The collective-coordinate method, remarkably successful in SU(3), is extended to the general SU( n) Skyrme model. The extension is nontrivial because for n ⩾ 4 in addition to the Wess-Zumino-Witten constraints qualitatively new constraints appear. The baryonic eigenstates obeying all the constraints are constructed in a systematical and definite procedure. These states may serve as a basis for the exact diagonalization of the symmetry breaking. The standard symmetry breakers are compatible with the constraints and lead to the correct order of magnitude of the baryon multiplet splitting.