We show that testing Bell inequalities in $W^\pm$ pair systems by measuring their angular correlation suffers from the ambiguity in kinetical reconstruction of the di-lepton decay mode. We further propose a new set of Bell observables based on the measurement of the linear polarization of the $W$ bosons that can be used in the semi-leptonic decay mode of $W^\pm$ pair, and we analyze the prospects of testing the violation of Bell inequalities at $e^+ e^-$ colliders.