A hyperaccretion flow around a stellar mass black hole is thought to be the most plausible engine that powers gamma-ray bursts (GRBs). The flow efficiently cools via neutrino emission at greater than or similar to 0.003-0.01 M-circle dot s(-1) (corresponding to a luminosity of similar to 10(50) erg s(-1)), while neither neutrino nor photon emission is efficient below this rate, so the flow should be advection-dominated. We carefully solve how a transition occurs from the advection-dominated to the neutrino-dominated branches, and find that the slope of the thermal equilibrium curve is negative in the surface density-accretion rate (Sigma-(M)over dot) plane, a condition for viscous instability, at radii smaller than similar to 12 R-g (with R-g being the gravitational radius). We also confirm that the flow is thermally stable. The consequence of this instability is the formation of a clumpy structure in the flow. This is because the larger (respectively smaller) surface density is, the smaller (respectively larger) the mass accretion rate from the region in question becomes, leading to growth of the density contrast. The timescale for clump formation is estimated to be shorter than 0.1 s. The observational implication is discussed in the context of GRBs. We suggest that this might explain the origin of the large variability observed in the prompt emission of GRBs.