  Zinc is a good indicator of metallicity in Damped Lyman alpha (DLA) systems
because it is almost unaffected by dust depletion. However, the use of zinc as
a tracer of metallicity evolution has been hampered by the difficulty of
detecting the Zn II resonance lines at high redshift. The measurement of zinc
abundance in a DLA system at z_abs > 3 obtained by means of the UVES
spectrograph at the VLT prompted us to re-analyse the full sample of zinc
abundances present in the literature to search for a metallicity-redshift
relation in DLA systems. The study of the metallicities of individual systems
shows evidence for an anti-correlation between [Zn/H] and redshift supported by
different types of statistical tools. The zinc metallicity decreases by -0.3
+/- 0.1 dex per unit redshift interval in the range 0.5 <~ z_abs <~ 3.5. This
rate is in good agreement with that found by Savaglio, Panagia & Stiavelli
(2000) in their recent study of DLA abundances corrected for dust depletion.
The present result does not require a knowledge of the dust depletion
pattern(s) in DLA systems. On the other hand, the analysis of the
column-density weighted metallicity of the sample, <Z>, does not show a clear
evidence for redshift evolution, consistent with previous studies of zinc
abundances. We propose that the apparent lack of evolution of <Z> is due to the
combination of selection bias effects together with the extreme sensitivity of
<Z> to low-number statistics.
