  Gamma-ray bursts (GRBs) have long been proposed as a complementary probe to
type Ia supernovae (SNe Ia) and cosmic microwave background to explore the
expansion history of the high-redshift universe, mainly because they are bright
enough to be detected at greater distances. Although they lack definite
physical explanations, many empirical correlations between GRB isotropic
energy/luminosity and some directly detectable spectral/temporal properties
have been proposed to make GRBs standard candles. Since the observed GRB rate
falls off rapidly at low redshifts, thus preventing a cosmology independent
calibration of these correlations. In order to avoid the circularity problem,
SN Ia data are usually used to calibrate the luminosity relations of GRBs in
the low redshift region (limited by the redshift range for SN Ia sample), and
then extrapolate it to the high redshift region. This approach is based on the
assumption of no redshift evolution for GRB luminosity relations. In this work,
we suggest the use a complete quasar sample in the redshift range of
$0.5<z<5.5$ to test such an assumption. We divide the quasar sample into
several sub-samples with different redshift bins, and use each sub-sample to
calibrate the isotropic $\gamma$-ray equivalent energy of GRBs in relevant
redshift bins. By fitting the newly calibrated data, we find strong evidence
that the most commonly used Amati relation between spectral peak energy and
isotropic-equivalent radiated energy shows no, or marginal, evolution with
redshift. Indeed, at different redshifts, the coefficients in the Amati
relation could have a maximum variation of 0.93\% at different redshifts, and
there could be no coincidence in the range of 1$\sigma$.
