  The CKM matrix describing quark mixing with three generations can be
parameterized by three Euler mixing angles and one CP violating phase. In most
of the parameterizations, the CP violating phase chosen is not a directly
measurable quantity and is parametrization dependent. In this work, we propose
to use the most accurately measured CP violating angle $\beta$ in the unitarity
triangleas the phase in the CKM matrix, and construct an explicit $\beta$
parameterization. We also derive an approximate Wolfenstein-like expression for
this parameterization.
