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