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.
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