  The global spin alignment of vector mesons is a powerful probe to study the
vorticity field of the system produced in non-central relativistic heavy-ion
collisions. Since the experimental observables of global spin alignment are
sensitive to many factors, proper corrections are need to be taken care of when
measuring the global spin alignment of vector mesons. In this paper, we propose
a method to correct the effect of finite pseudo-rapidity coverage when extract
the azimuthal dependence of spin alignment parameter $\rho_{00}$. The effects
of the finite pseudo-rapidity coverage on the azimuthal dependence of $\phi$
meson spin alignment and the potentially exist intrinsic spin alignment effects
are taken into consideration. The method presented in this paper is verified in
a Monte-Carlo simulation, it allows the measurements of azimuthal dependence of
global spin alignment to be conducted properly and accurately.
