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We prove that the finite exceptional groups F 4 (q), E 7 (q) ad , and E 8 (q) have no irreducible complex characters with Frobenius-Schur indicator −1, and we list exactly which irreducible characters of these groups are not real-valued. We also give an exact list of complex irreducible characters of the Ree groups 2 F 4 (q 2 ) which are not real-valued, and we show the only character of this group which has Frobenius-Schur indicator −1 is the cuspidal unipotent character χ 21 found by M. Geck.

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