  We propose an improved version of the redshift indicator developed by Atteia
(2003), which gets rid of the dependence on the burst duration and provides
better estimates for high-redshift GRBs. We present the derivation and the
definition of this redshift indicator, then its calibration with 17 GRBs with
known redshifts detected by HETE-2 and 2 more detected by Konus-Wind. We also
provide an estimation of the redshift for 59 bursts, and we finally discuss the
redshift distribution of HETE-bursts and the possible other applications of
this redshift indicator.
