Circular dichroism (CD) signals revealed in some materials may arise from different origins during measurements. Magnetic field dependent CD (MCD) emanating from the spin-polarized band provides direct insight into the spin-spin interband transitions in magnetic materials. On the contrary, natural CD effects which are artefactual signals resulting from the linear polarization (LP) components during the polarization modulation with a photo-elastic modulator in anisotropic polymer systems were usually observed. There is no simple method to reliably distinguish MCD effect due to spin polarized band structures from natural CD effect, which limits our understanding of the magnetic material/polymer hybrid structures. This paper aims to introduce a general strategy of averaging out the magnetic linear dichroism (MLD) contributions due to the anisotropic structure and disentangling MCD signal(s) from natural MCD signal(s). We demonstrate the effectiveness of separating MCD from natural MCD using rotational MCD measurement and presented the results of a sample with Co thin film on polymer Scotch tape (unplasticized polyvinyl chloride) glued on a quartz substrate. We demonstrate that the proposed method can be used as an effective tool in disentangling MCD and natural MCD effects, and it opens prospects to study the magnetic material /polymer hybrid systems.