The inversion of directions is an important operation with directions which plays an important role in qualitative spatial reasoning and spatial queries. In this work, we address on the inversion operation of the basic cardinal direction relations in the model of Goyal. The direction relation matrix model proposed by Goyal is a projection-based model for spatial direction relations between regions. This model is simple in calculation and easy to carry out formal reasoning, which is considered as currently one of the (...) most excellent models for representation and qualitative reasoning with cardinal direction relations in two-dimensional space. This work aims to realize the automatic inference and calculation of the inverse of the basic cardinal direction relations in the model of Goyal and further to improve the ability of spatial reasoning and spatial analysis of spatial database. In order to avoid the complicated manual reasoning, an algorithm for automatically performing the inverse operation on this model is devised by means of the operations of direction relation matrix. Theorems are provided to prove formally that our algorithm is correct and complete, which is also verified by comparing the result of our algorithm with that of manual reasoning for each basic cardinal direction relation. This study realized the automatic inference and calculation of the inverse of the basic cardinal direction relations in the model of Goyal and further improved the ability of spatial reasoning and spatial analysis of spatial database. (shrink)