  Kato's inequality is shown for the magnetic relativistic Schr\"odinger
operator $H_{A,m}$ defined as the operator theoretical {\it square root} of the
selfadjoint, magnetic nonrelativistic Schr\"odinger operator
$(-i\nabla-A(x))^2+m^2$ with an $L^{2}_{\text{\rm loc}}$ vector potential
$A(x)$.
