Given an integer n-dimensional lattice basis, the random sampling reduction was proven to find a short vector in $O(n^2(\frac{k}{6})^\frac{k}{4})$ arithmetic steps with an integer k, which is freely chosen by users. This paper introduces new random sampling reduction using precomputation techniques. The computation cost $O(k^2\log^2{k}(\frac{k}{6})^\frac{k}{4}+nk\log{k})$ is almost independent of the lattice dimension number. The new method is therefore especially advantageous to find a short lattice vector in higher dimensions. The arithmetic operation number of our new method is about 20% of the random sampling reduction with 200 dimensions, and with 1000 dimensions it is less than 1% $(\simeq {1}/{130})$ of that of the random sampling reduction with representative parameter settings under reasonable assumptions.