The potential energy surface of B4 has been studied ab initio using extended basis sets and coupled-cluster methods. The ground state (1A1g) is a singlet square that undergoes pseudo-Jahn-Teller distortion to a rhombic structure (1A(g)), but the energy gain is so small that the effective structure will be square at all practical temperatures. Total atomization energies SIGMA-D0 (kcal/mol) for B2 (62.2 +/- 2), B3 ( 189.1 +/- 2-192.6 +/- 2), and B4 (312.2 +/- 2) are computed by a modification of GAUSSIAN-1 (G1) theory. The validity of scaling and bond-additivity schemes for computing binding energies of higher clusters is discussed.