An apparatus and a method for non-invasively determining the blood oxygen saturation within a subject's tissue by near-infrared spectroscopy use the multi-distance method and take into account the attenuation of the light signal due to light absorbers other than hemoglobin and deoxyhemoglobin and the scattering properties of a subject's tissue. The apparatus and the method are particularly adapted for the measurement of blood oxygen saturation in the abdomen of newborns taking into account meconium, transitional stool, and biliverdin.