For many state-of-the-art cross section computations the standard approach of Feynman integral
reduction with the Laporta algorithm is the main bottleneck of the computation. We study a new
approach of Feynman integral reduction by introducing a block-triangular form, which is a smaller
system of equations compared to the system of equations which is generated with the Laporta
algorithm. The construction of the block-triangular form and its implementation in the program
Kira is the main interest of this report.