First Fit Decreasing is a classical bin packing algorithm: the items are ordered into their nonincreasing order, and then in this order the next item is always packed into the first bin where it fits. For an instance I let FFD(I) and OPT (I) denote the number of the used bins by algorithm FFD, and an optimal algorithm, respectively. We show in this paper that FFD(I) ≤ 11/9OPT (I) + 6/9, (1) and that this bound is tight. The tight bound of the additive constant was an open question for many years.