  We present a novel generalization of the Heisenberg uncertainty principle
which introduces the existence of a maximal observable momentum and at the same
time does not entail a minimal indeterminacy in position. The above result is
an exact generalized uncertainty principle (GUP), valid at all energy scales.
For small values of the deformation parameter $\beta$, our ansatz is consistent
with the usual expression for GUP borrowed from string theory, doubly special
relativity and other quantum gravity candidates that provide $\beta$ with a
negative sign. As a preliminary analysis, we study the implications of this new
model on some quantum mechanical applications and on the black hole
thermodynamics.
