When the terms of the series expansion for the gravitational potential of the Earth are expressed in terms of the orbital elements of an arbitrary Earth satellite, the orbital inclination,i, appears in each, term as the argument of a function of inclination only. For the special case when the field is axi-symmetric, studied in an earlier paper, a recurrence relation was given for a normalized inclination function,A k l(i), with two parameters. The present paper gives a recurrence relation for a general normalized function,K k lm(i), with three parameters.