An Euler correction method is developed for unsteady, transonic inviscid flows. The strategy of this method is to treat the flow-field behind the shock as rotational flow and elsewhere as irrotational flow. The solution for the irrotational flow is obtained by solving the unsteady full-potential equation using Jameson's rotated time-marching finite-difference scheme. Clebsch's representation of velocity is followed for rotational flow. In this representation the velocities are decomposed into a potential part and a rotational part written in terms of scalar functions. The potential part is computed from the unsteady full potential equation with appropriate modification based on Clebsch's representation of velocity. The rotational part is obtained analytically from the unsteady momentum equation written in terms of Clebsch variables. This method is applied to compute the unsteady flow-field characteristics for an oscillating NACA 64A010 aerofoil. The results of the present calculation are found to be in good agreement with both Euler solution and experimental results.