An effective algorithm is proposed to construct petrogenetical grids f
or multisystems. The algorithm is based on notions developed by V.A. Z
harikov and P. Laffite in 1961 concerning a multisystem as a section o
f an invariant pencil of the totality of component minerals. The affin
ities of independent reactions were chosen as equilibrium factors. In
this case, the directions of the Schreinemakers bundles coincide with
the reaction matrix vector-columns, which are treated as vectors in re
action affinity coordinates. All the relationships necessary to constr
uct a diagram in a plane for a multisystem as a section of a multidime
nsional invariant pencil are derived in the paper, and an example is g
iven as an illustration.