The Bethe-Salpeter equation (BSE) provides a non-perturbativ method of treatingrnthe relativistic two-particle bound state problems on the basis of covariant instantaneousrnansatz (CIA). On this basis, the structure of the hadron-quark vertex functionrnÀ€€(ˆq) of vector mesons is derived from a QCD motivated Bethe-salpeter (BS) framernwork and it is generalized to include various Dirac covariants (other than irn.") fromrntheir complete set. They are incorporated in accordance with a naive power countingrnrule order-by-order in powers of the inverse of the meson mass.rnWe study vector meson decay constants with inclusion of both the leading orderrn(LO) and the next-to-leading order (NLO) Dirac Covariants, in addition to irn.", inrnthe Hadron-Quark vertex function ð€€€(ˆq) from their complete set on the basis of powerrncounting rule through the frame work of BSE under covariant instantaneous ansatz