  The decay constants of pseudoscalar heavy mesons of $0^-$ state are computed
by means of the relativistic (instantaneous) Salpeter equation. We solved the
full Salpeter equation without making any further approximation, such as
ignoring the small component wave function. Therefore, our results for the
decay constants include the complete relativistic contributions from the light
and the heavy quarks. We obtain $F_{D_s} \approx 248 \pm 27 $, $F_{D} \approx
230 \pm 25 (D^0,D^\pm)$, $F_{B_s} \approx 216 \pm 32 $, $F_{B} \approx 196 \pm
29 (B^0,B^\pm)$, $F_{B_c} \approx 322 \pm 42 $ and $F_{\eta_c} \approx 292 \pm
25 $ MeV.
