A two dimensional anomaly cancellation argument is used to construct the SO(32) heterotic and type IIB membranes. By imposing different boundary conditions at the two boundaries of a membrane, we shift all of the two dimensional anomaly to one of the boundaries. The topology of these membranes is that of a 2-dimensional cone propagating in 11-dimensional Minkowski space. Dimensional reduction of these membranes yields the SO(32) heterotic and type IIB strings.