  Hypotheses of the universal seesaw mechanism and the {\it universal strength
for Yukawa couplings} are applied to explain one possible origin of
quasi-democratic mass matrices of a special type in a left-right symmetric
model with the gauge group $SU(3)_c\times SU(2)_L\times SU(2)_R\times U(1)$.
Two kinds of Higgs doublets are postulated to mediate scalar interactions
between the $i$-th generation of light fermion doublets and the $j$-th
generation of heavy fermion singlets with relative Yukawa coupling constants of
the exponential form $e^{i\phi_{ij}}$, where $\phi_{ij}$ are real phase
constants. The lowest seesaw approximation results effectively in self-adjoint
mass matrices which are quasi-democratic and have the same diagonal elements. A
set of values for the parameters $\phi_{ij}$ is found which reproduces the
present experimental data for the absolute values of the CKM matrix elements,
the Jarlskog parameter and the Wolfenstein parameters.
