An improved Lozi function with alternate coefficients has been proposed. The modi cations in the model allow to remove the holes in the attractor which are not desirable, but appeared in the previous Lozi function; in this way, an everywhere dense attractor can be obtained. Moreover, the strong sensitivity to the type of binarisation (conversion of real values to 0 and 1) has been demonstrated; this conversion to binary numbers is instrumental to apply the NIST tests for randomness. The results have been validated and compared via NIST tests, for the di erent methods of quantization. Finally, is has been veri ed that the random properties of the output signal have been improved thanks to the following strategies : under-sampling of the output signal, and the system order increasing.