  The reduction of a large number of scalar integrals to a small set of master
integrals via Laporta's algorithm is common practice in multi-loop
calculations. It is also a major bottleneck in terms of running time and memory
consumption. It involves solving a large set of linear equations where many of
the equations are linearly dependent. We propose a simple algorithm that
eliminates all linearly dependent equations from a given system, reducing the
time and space requirements of a subsequent run of Laporta's algorithm.
