Analytical expressions for the pair interaction potential between hydr
ogen atoms in a high magnetic held are derived for the triplet and sin
glet terms. The results are asymptotically exact for large interatomic
distance R compared with the atomic size and in the limit of ultrahig
h magnetic fields. It is shown that the ground state of the hydrogen m
olecule in a high magnetic field is the triplet term (3) Pi(u), which
corresponds to the case when one atom is in the ground state and the o
ther is in the first excited state. The interaction between two ground
-state hydrogen atoms in the term (3) Sigma(u) is very weak. The energ
y of the singlet term (1) Sigma(g) has a deep minimum, which is much h
igher than the triplet one and may be a metastable state of a hydrogen
molecule only.