In the following paper some properties of the atomic functions which are obtained by linear combination of $2 p$ with higher $p$-functions and which are used for building up molecular functions in the sense of the improved Hückel Theory-see Hartmann or Ruch [1, 2]-, are investigated. It is found that the atomic functions to be used for the M. O. of the bonding levels are less widely spread than the corresponding ones for the antibonding levels.