We experimentally demonstrated a new mechanism of generation of random pulses with the anomalous statistics (optical rogue waves) in a system of coupled Raman lasers. The pump laser with a linear cavity and wavelength of 1550 nm was coupled to a random laser generating nearby 1670 nm. These rogue waves appeared as a result of the interactions between Raman cascades and a coupling of the orthogonal states of polarization (SOPs). The desynchronization of SOPs caused by polarization instability led to chaotic oscillations. Due to the antiphase dynamics in two cascades, these chaotic oscillations were transformed into anomalous spikes satisfying rogue waves criteria.