Primary recrystallization textures were examined in the 84% and 95% cold-rolled boron-free Ni3Al single crystals with a Goss texture using the electron backscatter diffraction method. It was found that the main components of the textures in the specimens heat-treated at 873K/0.5h had a 40° rotation relationship about <111> to the original, Goss texture. All the eight variants of 40°<111> rotated grains existed. However, the number density is not even but dependent on whether the rotation axis is identical to the normal of slip planes activated during the prior cold rolling. The ratio of the number density among the variants was same in both the 84% and 95% cold-rolled foils. Based on these results, the formation of these 40°<111> rotated grains was explained assuming the modified multiple twinning mechanism where the annealing twinning occurred at the activated slip planes, followed by the subsequent twinning.