  M Handel has proved in [Topology 38 (1999) 235--264] a fixed point theorem
for an orientation preserving homeomorphism of the open unit disk, that may be
extended to the closed disk and that satisfies a linking property of orbits. We
give here a new proof of Handel's fixed point theorem, based on Brouwer theory
and some plane topology arguments. We will slightly improve the theorem by
proving the existence of a simple closed curve of index 1. This index result
was known to be true under an additional hypothesis and has been used by
different authors (J Franks [NYJM 2 (1996) 1--19, Trans.AMS 348 (1996)
2637--2662] S Matsumoto [Topol. Appl. 104 (2000) 191--214]) to study
homeomorphisms of surfaces.
