  Standard model is minimally extended using the unitary group $G'=U(3)\times
SU(2)\times U(1)$ of Connes' color-flavor algebra. In place of Connes'
unimodularity condition an extra Higgs is assumed to spontaneously break $G'$
down to standard model gauge group. It is shown that the theory becomes
anomaly-free only if right-handed neutrino is present in each generation. It is
also shown that the extra Higgs gives rise to large Majorana mass of
right-handed neutrino and the model contains new vectorial neutral current.
