We considered stability of the dimer of oxalic acid. The global minimum energy structure identified by us is stabilized by two inter- and four intramolecular hydrogen bonds, whereas the most stable structure identified in previous studies is supported by two inter- and three intramolecular hydrogen bonds. The latter structure proves to be less stable by 25 meV than the former. The global minimum stability results from a balancing act between a moderately attractive two-body interaction energy and small repulsive one-body terms. We have analyzed zero-point vibrational corrections to the stability of various conformers of oxalic acid and their dimers. We have found that minimum energy structures with the most stabilizing sets of hydrogen bonds have the largest zero-point vibrational energy, contrary to a naive anticipation based on red shifts of OH stretching modes involved in hydrogen bonds.