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Giles et al. (1995) have proven that Fahlman's recurrent cascade correlation (RCC) architecture is not capable of realizing finite state automata that have state-cycles of length more than two under a constant input signal. This paper extends the conclusions of Giles et al. by showing that there exists a corollary to their original proof which identifies a large second class of automata, that is also unrepresentable by RCC.