A study is made of convection in an anisotropic porous medium saturated with water near 4 degreesC, temperature at which the density reaches its maximum value. The saturated porous medium is contained in a square cavity with adiabatic horizontal walls and side walls subject to uniform temperatures. The parameters involved are the ratio of the extremum permeabilities K*, the anisotropic angle a giving the inclination of the principal axes, the Rayleigh number R and the inversion parameter gamma, this last parameter being related to the horizontal position of the pure conduction 4 degreesC isotherm relatively to the vertical walls. The problem is solved on the basis of the Darcy model and the Boussinesq approximation through the use of a finite difference numerical approach. For the case where the principal axes are parallel and perpendicular to the gravity vector, the Nusselt number is found to be maximum when the maximum permeability is in the Vertical direction. For cases with oblique axes, no symmetric flow and temperature fields can be obtained at gamma = 1 (pure conduction 4 degreesC isotherm midway between the two side walls), as it is the case for an isotropic porous medium. Moreover, another difference with the isotropic case is the fact that the minimum Nusselt number does not occur at gamma = 1 but at a value slightly different.