  In this paper we give an exact invariant for a relativistic linear harmonic
oscillator with time-dependent frequency. This is accomplished, following
Eliezer and Gray \cite{EliezerGray}, for the non-relativistic case, by
associating a relativistic plane isotropic harmonic oscillator with this
problem. This exact invariant reflects the conservation of angular momentum of
the associated relativistic plane isotropic oscillator. Departures in the
physical interpretations of this exact invariant caused by relativistic effects
are pointed out.
