  Unital qubit Schwarz maps interpolate between positive and completely
positive maps. It is shown that relaxation rates of qubit semigroups of unital
maps enjoying Schwarz property satisfy the universal constraint which provides
a modification of the corresponding constraint known for completely positive
semigroups. As an illustration we consider two paradigmatic qubit semigroups:
Pauli dynamical maps and phase covariant dynamics. This result has two
interesting implications: it provides a universal constraint for the spectra of
qubit Schwarz maps and gives rise to a necessary condition for a Schwarz qubit
map to be Markovian.
