  We use a nearly complete sample of Gamma Ray Bursts (GRBs) detected by the
Swift satellite to study the correlations between the spectral peak energy Ep
of the prompt emission, the isotropic energetics Eiso and the isotropic
luminosity Liso. This GRB sample is characterized by a high level of
completeness in redshift (90%). This allows us to probe in an unbiased way the
issue related to the physical origin of these correlations against selection
effects. We find that one burst, GRB 061021, is an outlier to the Ep-Eiso
correlation. Despite this case, we find strong Ep-Eiso and Ep-Liso correlations
for the bursts of the complete sample. Their slopes, normalisations and
dispersions are consistent with those found with the whole sample of bursts
with measured redshift and Ep. This means that the biases present in the total
sample commonly used to study these correlations do not affect their
properties. Finally, we also find no evolution with redshift of the Ep-Eiso and
Ep-Liso correlations.
