  We introduce a ZX-like diagrammatic language devoted to manipulating real
matrices - and rebits -, with its own set of axioms. We prove the necessity of
some non trivial axioms of these. We show that some restriction of the language
is complete. We exhibit two interpretations to and from the ZX-Calculus, thus
showing the consistency between the two languages. Finally, we derive from our
work a way to extract the real or imaginary part of a ZX-diagram, and prove
that a restriction of our language is complete if the equivalent restriction of
the ZX-calculus is complete.
