We have developed a systematic method on the basis of statistical testing of hypotheses to deal with the problem of identification of absorption redshift systems in the spectra of highredshift QSOs. We have taken account of Bahcall's signal-to-noise ratio /1/. Our procedure consists of the following steps: 1) Set up the identification criteria. 2) Divide the whole redshift ranges into intervals, within each of which the composition of the "visible" set of reference lines is the same. Search on the computer the spectrum at a steplength ∆z and count the number of systems supported by 1,2,3… identified lines. 3) For each visible set, calculate the probabilities of random identifications. 4) For each visible set, apply the statistical test to isolate the systems which are in the rejection region of the null-hypothesis. 5) Pick out those systems with high values of the signal-to-noise ratio from amongst the resulting systems in the last step. 6) Apply astrophysical considerations to the surviving systems. This last step will be discussed in a separate paper /10/.