This work aims at a geometrical semimicroscopic model to study the reentrant isotropic-nematic phase transition. It will be assumed that the micellar change of shape in lyotropics can be understood as the deformation of an ellipsoid which is assumed to have the idealized form of a micelle. It will be shown that such deformation is characterized by two kinds of quantities. The first one, which is a scalar determined by the ellipsoidal eccentricity, gives the intensity of the ellipsoidal deformation. The second one, which has a tensorial nature, describes the spatial distribution of such deformation and is proportional to the tensorial nematic order parameter. We construct the invariants of such deformation and couple it with the orientational order parameter to study the reentrant isotropic-nematic phase transition. We determine the thermodynamical characteristics of this phase transition and shown that it is a second-order phase transition. By comparing the theory so constructed with the experimental data, the parameters of the model will be determined.