  Self-consistent excited states of condensates are solutions of the
Gross-Pitaevskii (GP) equation and have been amply discussed in the literature
and related to experiments. By introducing a more general mean-field which
includes the GP one as a special case, we find a new class of self-consistent
excited states. In these states macroscopic numbers of bosons reside in
different one-particle functions, i.e., the states are fragmented. Still, a
single chemical potential is associated with the condensate. A numerical
example is presented, illustrating that the energies of the new, fragmented,
states are much lower than those of the GP excited states, and that they are
stable to variations of the particle number and shape of the trap potential.
