A new type of hydrogen bond, called a dihydrogen bond, has recently been introduced. In this bond a hydrogen is donated to another (hydridic) hydrogen-We apply a set of criteria developed in the context of the theory of "atoms in molecules" that were previously successfully used to study conventional hydrogen bonds. This method enables one to characterize the dihydrogen bond on the basis of the electron density only. We investigated a dimer structure of BH3NH3 at the ab initio level which contains two dihydrogen bonds that differ in strength. The combination of a theoretical density with our hydrogen-bonding criteria turns out to be a valuable new and independent source of information complementary to techniques such as NMR, IR, and structural crystallography.