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Vertical Cavity Surface-Emitting Laser (VCSEL) may exhibit bistability between two orthogonal polarization emissions [1]. Hysteresis has been reported in a narrow range of pumping current [2]. In this contribution we consider a VCSEL with negligible dichroism, where bistability is extended to the whole range of biasing current, from threshold to absolute maximum biasing rate. In practice two polarisation-resolved light-current curves coexist (Fig.1). The polarization emission state can be controlled by perturbing the VCSEL with crossed polarisation reinjection (XPR) pulses or feedback pulses. While an XPR pulse may induce a jump from situation depicted by Fig. 1, left panel, to situation depicted in Fig. 1, right panel, a feedback pulse can induce the reverse jump of the polarisation state. The temperature of the device can be used as a second parameter in order to vary the degree of stability of one component with respect to the other. We are not aware of any previous observation of such robust polarisation bistability.