Let *G* be a group and *t* an unknown. In this paper we prove that the equation *atbtct*^{−1}*dt*^{−1} = 1 (*a,b,c,d* ɛ *G*, *a*^{2} ≠ 1, *c*^{2} ≠ 1, *bd* ≠ 1) has a solution over *G*. This forms part of a program to investigate precisely when an equation, whose associated star graph contains no admissible paths of length less than 3, fails to have a solution over *G*.