The new relativistic WKB expression for leptonic decay widths of the vector mesons
as the relativistic component system of two fermions of arbitrary masses interacting
by means of the funnel-type potentials is obtained. Quasipotential equation is solved
by the WKB approximation. The behavior of the relativistic leptonic decay widths
of vector mesons was investigated. Comparison of the behavior for new expression
with its relativistic spinless analogue is given. Consideration is conducted within
the framework of completely covariant quasipotential approach in the Hamiltonian
formulation of quantum field theory, via a transition to the relativistic configurational
representation in the case of two relativistic spin particles of arbitrary masses.