  We construct a Lie 3-algebra extended model of the IIB matrix model. It
admits any Lie 3-algebra and possesses the same supersymmetry as the original
matrix model, and thus as type IIB superstring theory. We examine dynamics of
the model by taking minimal Lie 3-algebra that includes u(N) Lie algebra as an
example. There are two phases in the minimally extended model at least
classically. The extended action reduces to that of the IIB matrix model in one
phase. In other phase, it reduces to a more simple action, which is rather easy
to analyze.
