  We consider D3 branes at orbifolded conifold singularities which are not
quotient singularities. We use toric geometry and gauged linear sigma model to
study the moduli space of the gauge theories on the D3 branes. We find that
topologically distinct phases are related by a flop transition. It is also
shown that an orbifold singularity can occur in some phases if we give
expectation values to some of the chiral fields.
