  A new mathematical framework for the diagonalization of the nondiagonal
vector--scalar and axial-vector--pseudoscalar mixing in the effective meson
Lagrangian is described. This procedure has unexpected connections with the
Hadamard product of $n\times n$ matrices describing the couplings, masses, and
fields involved. The approach is shown to be much more efficient as compared
with the standard methods employed previously. The difference is especially
noticeable if the chiral symmetry is broken explicitly. The paper ends with an
illustrative application to the chiral model with broken $SU(3)_L\times
SU(3)_R$ symmetry.
