A new approach to joint regression analysis, entitled Trimmed Joint Regression (TJR), is proposed in which the adjustment of the linear relative-yield pattern of the cultivars is trimmed from the residues which can be attributed to a "specific interaction". The ranking of the residues to the joint regressions for each cultivar, within each trial, is analysed by the Friedman test to ascertain if they belong to the same parental distribution of the population of residues, for the different genotypes. The rejection of the null hypothesis is envisaged as the result of an organized pattern of the residues, due to a "specific interaction", and the genotypes responsible for such interactions are identified. The trimming method consists of the assessment of the linear regressions, after a reassessment of data related with "specific interactions". The increased accuracy which can be achieved is shown in a numerical example where the high repeatability of the method is illustrated by means of a comparison of the estimated yields for 1- and 2-year trials.