The nematic phases of a lyotropic system NadS/ decanol/ heavy water are investigated using optical conoscopy and image processing. The phase diagram obtained from these lyotropic materials predicts the occurrence of a direct phase transition, which does not present the biaxial nematic phase, between the discotic (N-D) and calamitic (N-C) nematic phases. A biaxial nematic (N-B) phase is optically characterized and confirmed through conoscopic image, inside the biaxial range, between the two uniaxial nematic phases. Also, their respective transition points are determined by means of image processing. The N-B phase observed here is discussed as part of the nature of the micellar configuration of lyotropic materials which exhibit uniaxial nematic phases.