  In this paper we discuss the concept of relational system with involution.
This system is called orthogonal if, for every pair of non-zero orthogonal
elements, there exists a supremal element in their upper cone and the upper
cone of orthogonal elements $x,\,x'$ is a singleton (i.e. $x,\,x'$ are
complements each other). To every orthogonal relational system can be assigned
a groupoid with involution. The conditions under which a groupoid is assigned
to an orthogonal relational systems are investigated. We will see that many
properties of the relational system can be captured by the associated groupoid.
Moreover, these structures enjoy several desirable algebraic features such as,
e.g., a direct decomposition representation and the strong amalgamation
property.
