We extend our recent work, in which the Dirac equation with a "(asymptotically free) Coulomb + (Lorentz scalar γ 0 σr) linear " potential is used to obtain the light quark wavefunction for qQ mesons in the limit m Q → ∞, to estimate the decay constant f P and the mixing parameter B of the pseudoscalar mesons. We compare our results for the evolution of f P and B with the meson mass M P to the non-relativistic formulas for these quantities and show that there is a significant correction in the subasymptotic region. For σ = 0.14 GeV −2 and Λ M S = 0.240 GeV we obtain: f D = 0.371 , f Ds = 0.442 , f B = 0.301 , f Bs = 0.368 GeV and B D = 0.88 , B Ds = 0.89 , B B = 0.95 , B Bs = 0.96 , and B K = 0.60.