An invariant for symplectic involutions on central simple algebras of degree divisible by~$4$ over fields of characteristic different from~$2$ is defined on the basis of Rost's cohomological invariant of degree~$3$ for torsors under symplectic groups. We relate this invariant to trace forms and show how its triviality yields a decomposability criterion for algebras of degree~$8$ with symplectic involution.