This paper describes a new way to reconstruct and identify muons with high efficiency and high pion rejection. Since muons at the ILC are often produced with or in jets, for many of the physics channels of interest[1], an efficient algorithm to deal with the identification and separation of particles within jets is important. The algorithm at the core of the method accounts for the effects of the magnetic field and for the loss of energy by charged particles due to ionization in the detector. We have chosen to develop the analysis within the setup of one of the Linear Collider Concept Detectors adopted by the US. Within b-pair production jets, particles cover a wide range in momenta; however ~ 80% of the particles have a momentum below 30 GeV[2]. Our study, focused on bbar-b jets, is preceded by a careful analysis of single energy particles between 2 and 50 GeV. As medium energy particles are a substantial component of the jets, many of the particles lose part of their energy in the calorimeters and the solenoid coil before reaching the muon detector where they may have energy below 2 GeV. To deal with this problem we have implemented a Runge-Kutta correction of the calculated trajectory to better handle these lower energy particles. The multiple scattering and other stochastic processes, more important at lower energy, is addressed by a Kalman-filter integrated into the reconstruction algorithm. The algorithm provides a unique and powerful separation of muons from pions. The 5 Tesla magnetic field from a solenoid surrounds the hadron calorimeter and allows the reconstruction and precision momentum measurement down to a few GeV
