Relative elemental abundances , and in particular the \alpha /Fe ratio , are an important diagnostic tool of the chemical evolution of damped Ly \alpha systems ( DLAs ) . The S/Zn ratio is not affected by differential dust depletion and is an excellent estimator of the \alpha /Fe ratio . We report 6 new determinations of sulphur abundance in DLAs at z _ { abs } \geq 2 with already known zinc abundances . The combination with extant data from the literature provides a measure of the S/Zn abundance ratio for a total of 11 high redshift DLA systems . The observed [ S/Zn ] ratios do not show the characteristic [ \alpha /Fe ] enhancement observed in metal-poor stars of the Milky Way at comparable level of metallicity ( [ Zn/H ] \approx - 1 ) . The behaviour of DLAs data is consistent with a general trend of decreasing [ S/Zn ] ratio with increasing metallicity [ Zn/H ] . This would be the first evidence of the expected decrease of the \alpha /Fe ratio in the course of chemical evolution of DLA systems . However , in contrast to what observed in our Galaxy , the \alpha /iron-peak ratio seems to attain solar values when the metallicity is still low ( [ Zn/H ] \leq –1 ) and to decrease below solar values at higher metallicities . The behaviour of the \alpha /Fe ratio challenges the frequently adopted hypothesis that high redshift DLAs are progenitors of spiral galaxies and favours instead an origin in galaxies characterized by low star formation rates , in agreement with the results from imaging studies of low redshift DLAs , where the candidate DLA galaxies show a variety of morphological types including dwarfs and LSBs and only a minority of spirals .