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We present an experimental study on the double <i>K</i>-shell ionization of argon in single collisions with the Xe⁵⁴⁺ ion at 197 MeV/u. The X-ray spectra of multi-ionized argon are measured at the observation angles of 90° and 145° with respect to the projectile beam. The target <i>K</i> X-ray satellite and hypersatellite lines are analyzed with a fitting model and the cross-section ratio of double to single <i>K</i>-shell ionization is derived. The experimental results are compared to the relativistic time-dependent, two-center calculations, and a reasonable agreement is reached.