  We demonstrate the conventional Jarzynski relation (JR) is violated for a
non-Markovian process with colored noise. As an example an exactly soluble
model is considered with a simple protocol for the external work performed on
the system along a non-equilibrium trajectory. For that model we derive an
exact expression for the dissipative energy in terms of an arbitrary correlator
of the noise characterized by an autocorrelation time $t_c$. As the result we
find corrections to the JR in terms of $t_c$. In the limiting case of a
Gaussian process as well as an infinitely slow process the conventional JR is
retained. The result is valid for an arbitrary colored noise.
