Abstract: The concept of block determinant \mathrmD\mathrme\mathrmt operation of multi-lateral matrices is explained, and the basic theorem of block determinant \mathrmD\mathrme\mathrmt operation of multi-lateral matrix section is proved. Some algebraic properties of block determinant \mathrmD\mathrme\mathrmt operation of multi-lateral matrices are given. As the application domain of this concept, the relationship between block determinant \mathrmD\mathrme\mathrmt operation and block tracing \mathrmT\mathrmr operation of multilateral matrix is explored.