  The Sturmian expansion of the generalized Dirac--Coulomb Green function
[R.\/~Szmytkowski, J.\ Phys.\ B \textbf{30}, 825 (1997); \textbf{30}, 2747(E)
(1997)] is exploited to derive a closed-form expression for the magnetizability
of the relativistic one-electron atom in an arbitrary discrete state, with a
point-like, spinless and motionless nucleus of charge $Ze$. The result has the
form of a double finite sum involving the generalized hypergeometric functions
${}_3F_2$ of the unit argument. Our general expression agrees with formulas
obtained analytically earlier by other authors for some particular states of
the atom. We present also numerical values of the magnetizability for some
excited states of selected hydrogenlike ions with $1 \leqslant Z \leqslant 137$
and compare them with data available in the literature.
