For k a field of characteristic 2, we show that there is a unique continuous automorphism of order 4 of the power series ring k[[t]] which sends t to t + t^2 + (t^6) + (t^{ 12} + t^{ 14}) + (t^{ 24} + t^{ 26} + t^{ 28} + t^{ 30}) + ... . For j >= 0, the j-th sum in parentheses has 2^j terms beginning at t^{ 6*2^j}, with successive terms in the j-th sum raising the exponent of t by 2.
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