An important aspect of improving perturbative predictions in high energy
physics is efficiently reducing dimensionally regularised Feynman integrals
through integration by parts (IBP) relations. The well-known triangle rule has
been used to achieve simple reduction schemes. In this work we introduce an
extensible, multi-loop version of the triangle rule, which we refer to as the
diamond rule. Such a structure appears frequently in higher-loop calculations.
We derive an explicit solution for the recursion, which prevents spurious poles
in intermediate steps of the computations. Applications for massless propagator
type diagrams at three, four, and five loops are discussed
