In this paper we study the subgroups of 3-transposition groups generated by a set of four 3-transpositions. As a consequence we deduce that the smallest Fischer simple groupF22cannot be generated by four 3-transpositions and hence rank (F22:D) = 5 or 6, whereDis the conjugacy class of 3-transpositions inF22and rank (F22:D) denotes the minimum number of 3-transpositions inDgeneratingF22. This result is an extension of the work done by the author in [11].