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Not AvailableIn any scientific breeding programme for improvement of dairy cattle greater importance is attached to sire selection on account of the larger number of progenies that can be raised by a bull in his life time compared to a cow. As milk yield is a sex limited character, sire testing has to be based on the yields of the relatives of the bull. Indices based on such records proposed by different authors have been briefly reviewed and the merits and limitations of the two common indices widely in use, namely the simple daughter average index and the Intermediate index are examined and a new index called the corrected index comparatively free from some of these limitations is developed. The proposed index is obtained from the formula S= y – b(x-A) where y is the simple average of all the daughters of the given sire, x the average of the dams of these daughters, A the herd average and b the intrasire regression of daughter’s performance on that of its dam. By setting a simple genetic model, the expectations and the variances of the two common indices mentioned earlier, along with that of the proposed index, are derived. The nature of the bias involved in their use is examined and the relative efficiencies of the three indices assessed. It is shown that the gain in efficiency of the corrected index over the intermediate index is 30 per cent or more for a heritability of 0.5 or less. Even when the value of the heritability is more than 0.5 the corrected index proved to be more efficient although to a lesser degree. In so far as the simple daughter average index is concerned, it is subject to bias on account of the unequal levels of dams’ production, whereas the corrected index which is free from the bias has efficiency in no case lower than that of former. The superiority of the corrected index over the other two is also empirically verified with the help of data pertaining to sixty nine bulls from six herds. Situation arising due to more than one daughter with records available for each cow is discussed. Methods for adjusting for the inequality of lactation length and the order of lactation have also been discussed. The minimum number of daughter-dam pairs required to test a sire by the use of the proposed index has been examined.Not Availabl