  We present an improvement of the interacting string bit theory proposed in
hep-th/0206059, designed to reproduce the non-planar perturbative amplitudes
between BMN operators in N=4 gauge theory. Our formalism incorporates the
effect of operator mixing and all non-planar corrections to the inner product.
We use supersymmetry to construct the bosonic matrix elements of the light-cone
Hamiltonian to all orders in g_2, and make a detailed comparison with the
non-planar amplitudes obtained from gauge theory to order (g_2)^2. We find a
precise match.
