  We introduce the third independent exactly solvable hypergeometric potential,
after the Eckart and the P\"oschl-Teller potentials, which is proportional to
an energy-independent parameter and has a shape that is independent of this
parameter. The general solution of the Schr\"odinger equation for this
potential is written through fundamental solutions each of which presents an
irreducible combination of two Gauss hypergeometric functions. The potential is
an asymmetric step-barrier with variable height and steepness. Discussing the
transmission above such a barrier, we derive a compact formula for the
reflection coefficient.
