The stabilization mechanism of the filamentation instability for a light ion beam (LIB) penetrating plasma is investigated. For the stabilization of the filamentation instability, external magnetic field which is parallel to the direction of the light ion beam propagation is applied. Linear growth rates of filamentation instabilities in a light ion beam-plasma system with an external magnetic field were obtained by means of a dispersion relation. Numerical simulations were carried out using the particle-in-cell (PIC) method. The stabilizing mechanism of the filamentation instability is described. The theory and simulation comparisons illustrate the results. (author). 1 tab., 1 fig., 10 refs.