Abstract: The statistical characteristics of structural plane orientations in fractured rock mass are usually described by Fisher distribution model, which maps the normal direction determined by dip angle and dip direction to random points on a unit sphere. The classical Fisher model assumes that the random points satisfy the circular symmetrical distribution, but does not consider the antipodal symmetry of fractures, as the anti-normal direction represents the same fracture orientation. A simple modified formula was previously proposed, in which the probability density curve is extended to satisfy the normalization condition (the first class modified model). However, this model does not agree with the superposition characteristic of symmetrical samples and then needs to be further improved. In this study, the second class modified model is developed, based on the superposition rule of statistics for samples on a sphere following antipodal symmetry. Accordingly, a new probability distribution function is derived, which satisfies both the normalization condition and superposition principle. Theoretical calculations and case analyses indicate that: the error of the classical Fisher model is higher than 5% when the clustering factor, k, is smaller than 3, which should not be ignored; the error of the classical model is less than 1% when k is larger than 3, which could be ignored basically. The first class modified model increases the peak of the probability density curve, producing new errors, which is not applicable when k<5. The second class modified model incorporates the superposition characteristic of antipodal symmetrical samples, and is more applicable to improve the classic Fisher distribution model.