We investigate the viscosity driven instability in rotating relativistic stars by means of an iterative approach .
We focus on polytropic rotating equilibrium stars and impose an m = 2 perturbation in the lapse .
We vary both the stiffness of the equation of state and the compactness of the star to study those effects on the value of the threshold .
For a uniformly rotating star , the criterion T / W , where T is the rotational kinetic energy and W is the gravitational binding energy , mainly depends on the compactness of the star and takes values around 0.13 \sim 0.16 , which differ slightly from that of Newtonian incompressible stars ( \sim 0.14 ) .
For differentially rotating stars , the critical value of T / W is found to span the range 0.17 - 0.25 .
This is significantly larger than the uniformly rotating case with the same compactness of the star .
Finally we discuss a possibility of detecting gravitational waves from viscosity driven instability with ground-based interferometers .