  We examine low energy limit of $U(3)_L\times U(3)_R$ chiral theory of mesons
through integrating out fields of vector and axial-vector mesons. The effective
lagrangian for pseudoscalar mesons at $O(p^4)$ has been obtained, and five low
energy coupling constants $L_i(i=1,2,3,9,10)$ have been revealed. They are in
good agreement with the results of CHPT's at $\mu \sim m_\rho$.
