We present a new sample of 37 close major-merger galaxy pairs, selected from the 2-degree field redshift survey of the two-micron all-sky survey (2MASS) galaxies. The selection criteria for our near-infrared pairs are more closely related to galaxy mass (a very important parameter in galaxy evolution models) than those for optical selected samples. Our sample benefits enormously from the high homogeneity and accuracy of the 2MASS database, and false matchings are minimized by the essentially three-dimensional selection procedure. Taking into account the biases, we find that 1.96 (±0.4)% of galaxies are in close major-merger pairs. This indicates a local merging rate of 1.0%, in good agreement with the results in recent studies of optical selected pairs in the local universe. The results derived with our sample have high confidence.