A theorem concerning the stability of a particular non-Newtonian fluid has been proved by Genesky1). In the present paper, we have taken a more general non-Newtonian fluid characterized by the relation $$T = - pI + \alpha _1 A_1 + \alpha _2 A_2 + \alpha _3 A_{1^2 } $$ and it has been proved that the stability criterion for this fluid does not change. Further by takingα 2 = 0 we find that the existance of a point of inflection in the velocity profile of a steady one-dimensional basic flow is a necessary condition for the growth of a super-imposed two-dimensional disturbance. This is of interest that even in some special types of non-Newtonian flow, the existence of a point of inflection can be associated with the instability.