The high-resolution infrared spectrum of perchloric acid has been observed in the 700-750 cm^-1 region using the infrared beamline at the MAX-I electron storage ring in Lund, Sweden. The spectrum displays extensive rotational structure due to a type a band and is assigned to ν₅, the HO-ClO₃ stretch. Approximately 1100 transitions in H³⁵ClO₄ and ca. 300 in H³⁷ClO₄ have been fitted using single subband analysis, generating constants for transitions having the same K. The origin of H³⁵ClO₄ K = 3t series is found to be 726.9971(4) cm^-1. Rotationally resolved infrared line positions are now available for the identification of HClO₄ in the atmosphere, which may be produced by the heterogeneous oxidation of chlorine containing species in the stratosphere.