  We revisit our recursive model for the fragmentation of polarized quarks
based on the string+${}^3P_0$ mechanism of $q\bar{q}$ pair creation. We make a
different choice for one input function of the model that simplifies the
implementation in a Monte Carlo program. No new parameters are introduced, and
the relevant results are the same apart from the suppression of the
spin-independent correlations between successive quarks. In addition, the
present version is more suitable for an interface with external event
generators. The theoretical aspects and the simulation results obtained with a
stand alone program are discussed in detail and compared with those of the
previous version of the model.
