  Applying the Gordon-decomposition-like technique, the convective spin current
(CSC) is extracted from the total angular-momentum current. The CSC describes
the transport properties of the electron spin and is conserved in the
relativistic quantum mechanics approach where the spin-orbit coupling has been
intrinsically taken into account. Arrestingly, in the presence of external
electromagnetic field, the component of the convective spin along the field
remain still conserved. This conserved CSC is also derived for the first time
in the nonrelativistic limit using the Foldy-Wouthuysen transformation.
