  The powerful muon and tracker systems of the CMS detector together with
dedicated reconstruction software allow precise and efficient measurement of
muon tracks originating from proton-proton collisions. The standard muon
reconstruction algorithms, however, are inadequate to deal with muons that do
not originate from collisions. We present the design, implementation, and
performance of a dedicated cosmic muon track reconstruction algorithm, which
features pattern recognition optimized for muons that are not coming from the
interaction point, i.e. cosmic muons and beam-halo muons. To evaluate the
performance of the new algorithm, data taken during Cosmic Challenge phases I
and II as well as beam-halo muons recorded during the first LHC beam operation
were studied. In addition, a variety of more general topologies of cosmic muons
and beam-halo muons were studied using simulated data to demonstrate some key
features of the new algorithm.
