A numerical solution of the radiative transfer equation in spherically symmetric geometry is presented using integral operators within the framework of the discrete space theory and expressing the specific intensity in terms of the nodal values of the radius-angle mesh. The solution obtained satisfies the following tests: (1) the invariance of the specific intensity in a medium in which radiation is neither absorbed nor emitted, (2) the continuity of the solution in both angle and radial distribution, (3) a numerical proof showing the uniqueness of the solution, and (4) the condition of zero net flux in a scattering medium with one boundary having a specular reflector, and global conservation of energy. The solution is found to satisfy the above tests to the machine accuracy. 13 references.