  This paper presents an application of the TwO-Dimensional CORrelation
(TODCOR) algorithm to multi-order spectra. The combination of many orders
enables the detection and measurement of the radial velocities of very faint
companions. The technique is first applied here to the case of HD41004, where
the secondary is 3.68 magnitudes fainter than the primary in the V band. When
applied to CORALIE spectra of this system, the technique measures the secondary
velocities with a precision of 0.6 km/s and facilitates an orbital solution of
the HD41004B subsystem. The orbit of HD41004B is nearly circular, with a
companion of a 19 Jupiter masses (minimum mass). The precision achieved for the
primary is 10 m/s, allowing the measurement of a long-term trend in the
velocities of HD41004A.
