  In this article, we distinguish Siegel cuspidal eigenforms of degree two on
the full symplectic group from the signs of their Hecke eigenvalues. To
establish our theorem, we obtain a result towards simultaneous sign changes of
eigenvalues of two Siegel eigenforms. In the course of the proof, we also prove
that the Satake $p$-parameters of two different Siegel eigenforms are distinct
for a set of primes $p$ of density 1. The main ingredient to prove the latter
result is the theory of Galois representations attached to Siegel eigenforms.
