  The relativistic nuclear recoil corrections to the energy of the
$2p_{\frac{3}{2}}$ state of hydrogen-like and the $(1s)^{2}2p_{\frac{3}{2}}$
state of high $Z$ lithium-like atoms in all orders in $\alpha Z$ are
calculated. The calculations are carried out using the B-spline method for the
Dirac equation. For low $Z$ the results of the calculation are in good
agreement with the $\alpha Z$ -expansion results. It is found that the total
nuclear recoil contribution to the energy of the $(1s)^{2}2p_{\frac{3}{2}}-
(1s)^{2}2s$ transition in lithium-like uranium constitutes $-0.09\,eV$.
