A new spectroscopic technique for measuring the spectrum of transient molecules, named optical heterodyne magnetic rotation enhanced concentration modulation spectroscopy (OH-MR-CMS) is introduced. It combines optical heterodyne detection and magnetic rotation spectroscopy with the concentration modulation technique leading to greatly improved sensitivity. The concentration modulation spectroscopy (CMS) is suitable for the detection of the spectrum of short-lifetime transient molecules and excited state molecules. The optical heterodyne (OH) technique is used for eliminating the amplitude fluctuation noise from the laser source so as to realize the detection limit of the shot noise. The magnetic rotation (MR) technique makes a selective detection of paramagnetic molecules, so as to further improve the detection sensitivity. The principle of OH-MR-CMS is interpreted in detail and the technique is used to measure the absorption spectrum of the O2 b1Σ+g-X3Σ-g forbidden transition with a quite good signal-to-noise (S/N) ratio. The detailed analysis of the sensitivity of this technique is presented, the minimum relative absorption is approximately 1.9×10-9 and the absorption cross-section σ of the O2 forbidden transition is 2.4×10-24 cm2.