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Injection locking properties of a semiconductor laser have been analyzed, taking into account the injected carrier density dependent refractive index in the active region. It has been found that this dependence significantly affects the injection locking properties, giving rise to a peculiar asymmetric tuning curve and dynamic instability. The instability originates from the intermode interaction via the modulation in the injected carrier density caused by intensity beat. The detuning dependence of the direct modulation response characteristics inside and outside of the locking range have also been examined.