An elementary procedure is outlined for obtaining zero approximation eigenfunctions of many electron problems. The procedure allows a calculation of these functions as linear combinations of products of functions, each involving one electron only. The proper combinatin of products for one of the terms of highest multiplicity may, as a rule, be obtained by inspection; the remaining functions are obtained from this by the use of angular momentum operators. The "strong field" eigenfunctions for equivalent and non-equivalent electrons are obtained first, and from these are found the "weak field" eigenfunctions. The usual solution of the secular equation is unnecessary wherever the resultant states may be interpreted as having a definite and known kind of vector coupling (e.g. Russell-Saunders, or ($\mathrm{jj}$)).