Polarimetry in astrophysics had no much development in the hard X- and soft /spl gamma/-ray energy range; in fact no dedicated polarimeters had ever been launched in space. Previous Monte Carlo simulations and prototype experimental measurements were made in order to evaluate the polarimetric performances of pixelised CZT matrices. The results showed that CZT based polarimeters are able to perform polarimetric measurements of short duration polarised emissions like gamma ray bursts. On the behalf of a Gamma Ray Burst Monitor (GRBM) proposal for the LOBSTER experiment, approved by ESA for a Phase A study for a future flight (2009) aboard the International Space Station (ISS), we propose a Monte Carlo polarimetric study of the 4 detection units that compose this instrument. Each of these units is a 24/spl times/12 matrix of CZT elementary crystals. Each pixel has a cross section of 8/spl times/8 mm/sup 2/ , therefore a detection unit has an active area of about 184 cm/sup 2/. The detector thickness is 3 mm as baseline, and 5 mm in the case this thickness is crucial to exploit the GRBM as polarimeter as well. The 4 detection units have a rectangular FOV of 55/spl deg//spl times/35/spl deg/ FVVHM and their axes misaligned with each other by 45/spl deg/ in the direction perpendicular to the ISS motion and 10/spl deg/ along the ISS direction of motion. Energy dependent polarimetric Q factor and detection efficiencies will be determined. Expected GRBM minimum detectable polarisation will be presented and discussed.