  This paper proposes a new high-order generalized uncertainty principle, which
can modify the momentum operator and position operator simultaneously.
Moreover, the new form of GUP is consistent with the viewpoint of the existence
of the minimum length uncertainty and the maximum observable momentum proposed
by the mainstream quantum gravity theory. By using the new GUP, the maximum
localization state and position eigenfunction are discussed, and the
corresponding conclusions are compared with the existing literature. The
harmonic oscillator is further discussed at the end of this article as an
example.
