The paper gives further development of the method of a plate single-sided probe, which makes it possible to reconstruct the total electron velocity distribution function in an axially symmetric nonequilibrium plasma with an arbitrary degree of anisotropy. The method is improved for plasma diagnostics without the assumption of any symmetry. The theory of the method is developed and analytical relations are obtained connecting the Legendre components of the second-order derivative of the probe current with respect to the potential of the probe and the electron distribution function. The method is experimentally tested in the plasma of a positive column of a helium glow discharge. New possibilities of the method for investigating plasma near the boundaries are demonstrated and non-traditional information is obtained on the processes of escape of charged particles from the plasma volume on the walls.