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Let E be a real Banach space, and K a closed convex nonempty subset of E. Let T1,T2,…,Tm:K→K be m total asymptotically nonexpansive mappings. A simple iterative sequence {xn}n≥1 is constructed in E and necessary and sufficient conditions for this sequence to converge to a common fixed point of {Ti}i=1m are given. Furthermore, in the case that E is a uniformly convex real Banach space, strong convergence of the sequence {xn}n=1∞ to a common fixed point of the family {Ti}i=1m is proved. Our recursion formula is much simpler and much more applicable than those recently announced by several authors for the same problem.