The importance of properly taking into account the factorization scheme dependence of parton distribution functions is emphasized. A serious error in the usual handling of this topic is pointed out and the correct procedure for transforming parton distribution functions from one factorisation scheme to another recalled. It is shown that the conventional $\overline{\rm {MS}}$ and DIS definitions thereof are ill-defined due to the lack of distinction between the factorisation scheme dependence of parton distribution functions and renormalisation scheme dependence of the strong coupling constant $α_s$. A novel definition of parton distribution functions is suggested and its role in the construction of consistent next-to-leading order event generators briefly outlined.

PRA-HEP-93/05, Latex, 10 pages and 2 Postscript figures appended at the end of this file