A three component strap fastener having a body member with a fork inserted into a fork end opening and a catch inserted into an opposite catch end opening in the body member is improved by reconfiguring the catch end opening so as to prevent undesirable twisting of the catch relative to the fork within the body member. Additional constrainment of the catch to prevent it from being forced out of coplanar relationship relative to the fork is achieved by narrowing the outboard extremities of the open mouth formed at the catch end opening of the body member. This added constrainment is achieved by building up the interior wall structure of the body member at the transverse outboard extremities of the catch end opening with four interior, wedge-shaped corner restraints. These corner restraints are located at the transverse, outboard extremities of the catch end opening so that the mouth of the slit at the catch end opening has truncated, pointed corners, but otherwise has a uniform, narrow dimensional thickness between its corners.