A rotational shear flow is examined in the bounded parallel-plate geometry for a four-constant Oldroyd-type fluid which has a constant viscosity, and constant first and second normal stress coefficients. A new type of Galerkin spectral technique is introduced to solve the resulting two-dimensional stiff boundary value problem. We show that even a small second normal stress difference can lead to a significant increase (nearly 100%) in the stability of the base torsional flow. Beyond a critical Deborah number the secondary flow, in the form of travelling waves, appears to be confined between two critical radii, in qualitative agreement with the experimental results of Byars et al. (1994). The mechanism behind this instability is investigated for dilute polymer solutions.