  We examine the stability of self-similar solutions for an accelerating
relativistic blast wave which is generated by a point explosion in an external
medium with a steep radial density profile of a power-law index > 4.134. These
accelerating solutions apply, for example, to the breakout of a gamma-ray burst
outflow from the boundary of a massive star, as assumed in the popular
collapsar model. We show that short wavelength perturbations may grow but only
by a modest factor <~ 10.
