  Starting from a new zeroth order basis for quark mixing (CKM) matrix based on
the quark-lepton complementarity and the tri-bimaximal pattern of lepton
mixing, we derive a triminimal parametrization of CKM matrix with three small
angles and a CP-violating phase as its parameters. This new triminimal
parametrization has the merits of fast convergence and simplicity in
application. With the quark-lepton complementary relations, we derive relations
between the two unified triminimal parametrizations for quark mixing obtained
in this work and for lepton mixing obtained by Pakvasa-Rodejohann-Weiler.
Parametrization deviating from quark-lepton complementarity is also discussed.
