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In this paper, we develop a spectral differential technique with which the dynamical mass of low-mass companions can be found. This method aims at discovering close companions to late-type stars by removing the stellar spectrum through a subtraction of spectra obtained at different orbital phases and discovering the companion spectrum in the difference spectrum in which the companion lines appear twice (positive and negative signal). The resulting radial velocity difference of these two signals provides the true mass of the companion, if the orbital solution for the radial velocities of the primary is known. We select the CO line region in the K band for our study, because it provides a favourable star-to-companion brightness ratio for our test case GJ 1046, an M2V dwarf with a low-mass companion that most likely is a brown dwarf. Furthermore, these lines remain largely unblended in the difference spectrum so that the radial velocity amplitude of the companion can be measured directly. Only if the companion rotates rapidly and has a small radial velocity due to a high mass, does blending occur for all lines so that our approach fails. We also consider activity of the host star, and show that the companion difference flux can be expected to have larger amplitude than the residual signal from the active star so that stellar activity does not inhibit the determination of the companion mass. In addition to determining the companion mass, we restore the single companion spectrum from the difference spectrum using singular value decomposition. ((c) 2013 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)