The energy emission involved in a Gamma-Ray Burst evidently can be estimated only provided that we know the distance to the source. The same is true for the peak energy of the event in the source rest frame. Redshifts have been actually measured only for about 40 events. In order to check if it is possible to extend the Epeakrest E relation originally found by Amati et al. [Intrinsic spectra and energetics of BeppoSAX Gamma-Ray Bursts with known redshifts. Astron. Astrophys. 390, 81 89, 2002] to a larger number of events, we make use of the pseudo-redshift estimate proposed by Atteia [A simple empirical redshift indicator for Gamma-Ray Bursts. Astron. Astrophys. 407, L1 L4, 2003] and of the spectra published by Band et al. [BATSE observations of Gamma-Ray Burst spectra: I. Spectral diversity, ApJ 413, 281 292, 1993]. We thus obtain a completely independent set of events which indeed follows the same Epeakrest E relation and confirms it.