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Gamma-ray bursts (GRBs) have long been proposed as a complementary probe totype Ia supernovae (SNe Ia) and cosmic microwave background to explore theexpansion history of the high-redshift universe, mainly because they are brightenough to be detected at greater distances. Although they lack definitephysical explanations, many empirical correlations between GRB isotropicenergy/luminosity and some directly detectable spectral/temporal propertieshave been proposed to make GRBs standard candles. Since the observed GRB ratefalls off rapidly at low redshifts, thus preventing a cosmology independentcalibration of these correlations. In order to avoid the circularity problem,SN Ia data are usually used to calibrate the luminosity relations of GRBs inthe low redshift region (limited by the redshift range for SN Ia sample), andthen extrapolate it to the high redshift region. This approach is based on theassumption 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 intoseveral sub-samples with different redshift bins, and use each sub-sample tocalibrate the isotropic $\gamma$-ray equivalent energy of GRBs in relevantredshift bins. By fitting the newly calibrated data, we find strong evidencethat the most commonly used Amati relation between spectral peak energy andisotropic-equivalent radiated energy shows no, or marginal, evolution withredshift. Indeed, at different redshifts, the coefficients in the Amatirelation could have a maximum variation of 0.93\% at different redshifts, andthere could be no coincidence in the range of 1$\sigma$.

Redshift evolution of the Amati relation: calibrated results from the Hubble diagram of quasars at high redshifts