In this paper, we study nonblocking supervisory control of discrete event systems under partial observation. We introduce a weak normality condition defined in terms of a modified natural projection map. The weak normality condition is weaker than the original one and stronger than the observability condition. Moreover, it is preserved under union. Given a marked language specification, we present a procedure for computing the supremal sublanguage which satisfies Lm(G)-closure, controllability, and weak normality. There exists a nonblocking supervisor for this supremal sublanguage. Such a supervisor is more permissive than the one which achieves the supremal Lm(G)-closed, controllable, and normal sublanguage.