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Let $F$ be the category with the set of objects $\bf N$ and morphisms beingthe functions between the standard finite sets of the correspondingcardinalities. Let $Jf:F\rightarrow Sets$ be the obvious functor from thiscategory to the category of sets. In this paper we construct, for any relativemonad $\bf RR$ on $Jf$ and a left module $\bf LM$ over $\bf RR$, a C-system$C({\bf RR},{\bf LM})$ and explicitly compute the action of the B-systemoperations on its B-sets.  In the following paper it is used to provide a rigorous mathematical approachto the construction of the C-systems underlying the term models of a wide classof dependent type theories.  This paper is a result of evolution of arXiv:1407.3394. However this paper ismuch more detailed and contains a lot of material that is not contained inarXiv:1407.3394. It also does not cover some material that is covered inarXiv:1407.3394.

C-system of a module over a $Jf$-relative monad