The unsteady Couette flow with transpiration of a viscous fluid in a rotating system has been considered. An exact solution of the governing equations has been obtained by using Laplace Transform Technique. Solutions for velocity distributions and the shear stresses have been obtained for small time 𝝉= 𝟎. 𝟎𝟓 as well as large time 𝝉= 𝟏𝟎. 𝟎. it is found that for small times the primary velocity profile increases with decrease in 𝑲𝟐 with constant 𝑹𝒆 while the secondary velocity profile decreases with decrease in 𝑲𝟐. It is also found that for large times, the primary flow increases with increase in 𝑲𝟐, the secondary velocity behaves in an oscillatory manner near the moving plate and increases near the stationary plate. There exists a back flow in the region𝟎. 𝟎 ≪ 𝝋 ≪ 𝟏. 𝟎. The shear stress due to primary flow decreases with increase in 𝑲𝟐. On the other hand, it increases due to secondary flow with increase in rotation parameter with constant 𝑹𝒆 for small times. It is also observed that the shear stress for large time with constant 𝑹𝒆 shows layers of separation in both primary and secondary flow due to high rotation