A modest effort is made to study the unsteady two-fluid flow of blood in an arterial stenosis under the application of a transverse uniform magnetic field by adopting Frobenius series method. Plasma fluid in the region of peripheral layer and blood in the central region are considered as a Newtonian fluid in character. The Frobenius method has been adopted to solve the governing equation for the central region and obtain the expression of the velocity profile in that region. It is seen that when the values of hematocrit (m h) and Hartmann number (M) are increasing, the decrease in forwarding flow velocity and the rise in reversal (backward) flow velocity are observed. The axial velocity is increased due to an increase in the thickness of plasma layer. It is evident that the analytical values of velocity obtained from the present study are compared with the corresponding numerical results obtained from work done by Ponalagusamy and Tamil Selvi (Meccanica, 48(2013), 2427-2438), and there is a good agreement between them.