The formalism for triatomic reactive scattering using row-orthonormal hyperspherical coordinates is presented. The transformation properties of these coordinates under kinematic rotations and symmetry operations are derived, as is the Hamiltonian of the system. This formalism is compared with the one using symmetrized principal moment of inertia hyperspherical coordinates. Continuity conditions appropriate for the absence and presence of the geometric phase effect associated with conical intersections are considered. The potential application of these two sets of coordinates to tetraatomic systems is discussed. It is shown that the row-orthonormal coordinates are well suited for the treatment of systems of four or more atoms.