  The uniformly optimal search plan is a cornerstone of the optimal search
theory. It is well-known that when the target distribution is circular normal
and the detection function is exponential, the uniformly search plan has
several desirable properties. This article establishes that these properties
hold for any continuous target distribution. The results provide useful
information to the search team when they need to choose a non-circular normal
target distribution in a real-world search mission.
