Genotype-environment interaction arises when the ranking of genotypes changes under different environments. An alternative model was proposed to estimate the transmitting ability as a sum of a constant part common to two countries and a variable part (interaction effect) specific to each country. Separation of the constant part and the variable part in the alternative model is logical because the genes controlling a quantitative trait are unlikely to be all involved in genotype-environment interaction. The correlations between multiple-trait evaluations across countries and the transmitting abilities of the proposed alternative model were compared using a combination of four factors: 1) the size of interaction variance, 2) the number of daughters per sire, 3) the correlation of interaction effect between two countries, and 4) the availability of a sire's national evaluation in both countries. The results indicated that the correlation between the transmitting abilities of the alternative model and multiple-trait evaluations across countries was higher when sires had national evaluations in both countries rather than in either or neither country. The correlation between genetic evaluations of the two procedures dropped consistently when the number of daughters per sire changed from 100 to 30. The correlation between the two procedures in one country increased with increasing numbers of daughters in the other country. As the interaction variance increased, the correlation between the two procedures decreased, suggesting that it was important to take into account the genotype-environment interaction in global evaluations. Partition of sire effects into the constant and interaction parts permitted the combination of these two parts with different weights for international sire selection.