  In the models with vector like quark doublets, the mass matrices of up and
down type quarks are related. Precise diagonalization for the mass matrices
became an obstacle in the numerical studies. In this work we propose a
diagonalization method at first. As its application, in the standard model with
one vector like quark doublet we present quark mass spectrum, Feynman rules for
the calculation of $B\to X_s\gamma$. We find that i) under the constraints of
the CKM matrix measurements, the mass parameters in the bilinear term are
constrained to a small value by the small deviation from unitarity; ii)
compared with the fourth generation extension of the standard model, there is
an enhancement to $B\to X_s\gamma$ process in the contribution of vector like
quark, resulting a non-decoupling effect in such models.
