The optical magnetoelectric effect, which is an inherent attribute of the spin excitations in multiferroics, drastically changes their optical properties compared to conventional materials where light-matter interaction is expressed only by the dielectric permittivity and magnetic permeability. Our polarized absorption experiments performed on multiferroic Ca2CoSi2O7 and Ba2CoGe2O7 in the THz spectral range demonstrate that such magnetoeletric spin excitations show quadrochroism, i.e. they have different colours for all the four combinations of the two propagation directions (forward or backward) and the two orthogonal polarizations of a light beam. We found that quadrochroism can give rise to peculiar optical properties, such as one-way transparency and zero-reflection of these excitations, which can open a new horizon in photonics. One-way transparency is also related to the static magnetoelectric phenomena, hence, these optical studies can provide guidelines for the systematic synthesis of new materials with large dc magnetoelectric effect.