  We introduce a new generalization of the Pauli channels using the mutually
unbiased measurement operators. The resulting channels are bistochastic but
their eigenvectors are not unitary. We analyze the channel properties, such as
complete positivity, entanglement breaking, and multiplicativity of maximal
output purity. We illustrate our results with the maps constructed from the
Gell-Mann matrices and the Heisenberg-Weyl observables.
