The (2) (IIg)-I-3-A (IIu)-I-3 system of B-2 has been characterized for the first time. A full rotational analysis of the 0-0, 0-1, 1-0, and 1-3 bands has been performed. The molecular parameters are compared with recent high level theoretical calculations and show good agreement. An extensive perturbation of the upper (2) (IIg)-I-3 state by the (1) (IIg)-I-3 state was observed. This was most clearly evident for v=0 of the (2) (IIg)-I-3 state for the (BB)-B-10-B-11 isotopomer, which is split into two components by the interaction with v=7 of (1) (IIg)-I-3. The perturbation interaction exhibited a significant rotational dependence, which was interpreted as arising from a change in the Franck-Condon factors as the rotational contribution to the potential changed. A weak local perturbation was observed in v=1 of the A (IIu)-I-3 state from a crossing with v=2 of the alpha (5) Sigma(u)(-) state.