The transient and steady state behavior of a 1% DNA solution are studied using particle tracking velocimetry in Couette geometry for the shear rate range between 0.01 to 1000 s^-1. The velocity profiles for shear rates > O(1 s^-1) indicate an initial transient instability, which occurs during the stress overshoot, and permanent shear banding, which develops slowly after the stress undershoot. At very high shear rates, the permanent shear banding disappears and approximate linear velocity profile is restored.