  We prove that a generic multi-Higgs-doublet model (NHDM) generally must
contain terms in the potential that violate the custodial symmetry. This is
done by showing that the O(4) violating terms of the NHDM potential cannot be
excluded by imposing a symmetry on the NHDM Lagrangian. Hence we expect
higher-order corrections to necessarily introduce such terms. We also note, in
the case of custodially symmetric Higgs-quark couplings, that vacuum alignment
will lead to up-down mass degeneration; this is not true if the vacua are not
aligned.
