During late Tertiary time, the secular variation of the geomagnetic field vector at a number of widely separated sites can be modelled as the sum of the field vector of a randomly sampled isotropic normal dipole moment and a non-dipole field vector that is a function of the assumed source geometry. Here, the non-dipole field vector distribution is calculated in the limit for an infinite number of radial dipole sources on the core surface with a possible latitudinal bias in geographic distribution and a normal moment distribution that is invariant with respect to geographic location. The model therefore consists of four degrees of freedom, and for the usual case of unit vector data the number reduces to three because the dipole variance the and non-dipole source moment variance can be specified only as their ratios to the mean dipole moment. The resultant non-dipole field vectors are non-isotropically normal with zero mean (if and only if the mean of the source moment distribution is everywhere zero). For the assumed source geometry, the dipole-non-dipole sum is normally distributed with mean and covariance as functions of latitude. For direct comparison with the available directional data, the normal distribution is integrated over all possible vector magnitudes to yield the associated unconditional (unit vector) distribution.