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Abstract: This is the final paper in a series of four on fixed point ratios in non-subspace actions of finite classical groups. Our main result states that if G is a finite almost simple classical group and Ω is a faithful transitive non-subspace G-set then either for all elements of prime order, or is one of a small number of known exceptions. In this paper we assume is either an almost simple irreducible subgroup in Aschbacher''s collection, or a subgroup in a small additional set which arises when G has socle (q even) or . This completes the proof of the main theorem. [Copyright &y& Elsevier]