The powerful muon and tracker systems of the CMS detector together with sophisticated 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. In this note we present the design, implementation and performance results 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 were studied and compared with simulated cosmic data. 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
