Abstract: In Clifford algebra, the hyperbolic imaginary unit j(j²=1, j≠1, j^*= -j) was used to establish the hyperbolic Minkowski space. We can define the hyperbolic norm and algebra structure in the non\|Euclidean space, which can be applied to the discussion of the physical problem of relativity theory.

Key words: Clifford algebra, Minkowski space, semi-linear space,