Negami has already shown that there is a natural number N(F²) for any closed surface F² such that two triangulations on F² with n vertices can be transformed into each other by a sequence of diagonal flips if nN(F²). We investigate the same theorem for pseudo-triangulations with or without loops, estimating the length of a sequence of diagonal flips. Our arguments will be applied to simple triangulations to obtain a linear upper bound for N(F²) with respect to the genus of F².