  For a flat family of Du Val singularities, we can take a simultaneous
resolution after finite base change. It is an interesting problem to consider
this analogy for a flat family of higher dimensional canonical singularities.
In this note, we consider an existence of simultaneous terminalization for K.
Altmann's homogeneous toric deformation whose central fibre is an affine
Gorenstein toric singularity. We obtain examples that there are no simultaneous
terminalization even after finite base change and give a sufficient condition
for an existence of simultaneous terminalization. Some examples of
4-dimensional flop are obtained as an application.
