  In this paper, we focus on both analytical expressions of three and four
point integrals for the case of small Gram determinant and numerical
improvement of $n$-point integrals for $n\ge5$. Explicit expressions of three
and four-point integrals in the small Gram determinant region are provided by
the new method. Furthermore, $n$-point one-loop integral with $n\ge5$ is always
reduced to five number of $(n-1)$-point integrals regardless of how many points
are on a loop, which improves dramatically the CPU time consuming. Besides, the
theoretical and numerical error riginating from computing higher dimensional
Cayley matrix could be reduced by the dimension of the matrix being always
fixed to five. We suggest a general reduction formulae for five and more point
scalar, vector, and tensor integrals at one-loop level.
