We report on the observation of a new phenomenon occurring in a fiber ring laser. This phenomenon is about the transition from an initially bidirectional emission of a reciprocal fiber ring laser to a unidirectional emission at a certain pump power threshold. In addition, the final direction is not predefined but appears to be randomly chosen every time the threshold is exceeded. Therefore, we term this new phenomenon direction instability. Furthermore, we provide a first discussion of how the instability threshold is influenced by the length and the loss of the cavity. We show that the threshold follows a power times length scaling, indicating a nonlinear origin.