Abstract: The non-conforming displacement functions of refined direct stiffness methodare presented. With the application of IPT test, a new convergence test, which is calledstrong-IPT test, for separable(C￣0)non-conforming element is established. The test is asufficient one for the convergence and particularly it is valid for the(C￣0)refined element. Inaddition,a class of(C￣0)refined element are proposed and they are proven to pass strong-IPTtest.