In this paper we have studied the problem of the unsteady flow of an electrically conducting incompressible viscous fluid through a circular pipe under the influence of a uniform applied transverse magnetic field when the walls are non-conducting. It has been assumed that the velocity vanishes on the non-conducting walls and initially the fluid is at rest. The velocity field and the induced magnetic field are calculated by an iteration procedure and have been found up to second order terms inM (Hartmann number) which is taken to be small. We have also neglected the term involving β (= 4πμση/ρ) the self inductance of the fluid, which is valid for small values ofM.