This paper presents a new algorithm, TRIMOR, to analyse multi-order spectra of triple systems. The algorithm is an extension of TRICOR, the three-dimensional correlation technique that derives the radial velocities of triple stellar systems from single-order spectra. The combined correlation derived from many orders enables the detection and the measurement of radial velocities of faint tertiary companions. The paper applied TRIMOR to the already available spectra of HD188753, a well known triple system, yielding the radial velocities of the faintest star in the system. This rendered the close pair of the triple system a double-lined spectroscopic binary, which led to a precise mass-ratio and an estimate of its inclination. The close-pair inclination is very close to the inclination of the wide orbit, consistent with the assertion that this triple system has a close to coplanar configuration.
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