In Le Cam`s earlier work on superefficiency, it is proved that if an estimate is superefficient at a given parameter value θ_0, then there must exist an infinite sequence {θ_n} of values(converging to θ_0) at which this estimate is worse than M. L. E. for certain classes of loss functions. For one-dimensional cases, these classes of loss functions include squared error loss. However, for multi-dimensional cases, they do not. This note is to give an example where a superefficient estimator of a multi-dimensional parameter is not inferior to M. L. E. along any sequence {θ_n} converging to the point of superefficiency with respect to the squared error loss.