  Let $\mathcal{G}=[A & M N & B]$ be a generalized matrix algebra defined by
the Morita context $(A, B,_AM_B,_BN_A, \Phi_{MN}, \Psi_{NM})$. In this article
we mainly study the question of whether there exist proper Jordan derivations
for the generalized matrix algebra $\mathcal{G}$. It is shown that if one of
the bilinear pairings $\Phi_{MN}$ and $\Psi_{NM}$ is nondegenerate, then every
antiderivation of $\mathcal{G}$ is zero. Furthermore, if the bilinear pairings
$\Phi_{MN}$ and $\Psi_{NM}$ are both zero, then every Jordan derivation of
$\mathcal{G}$ is the sum of a derivation and an antiderivation. Several
constructive examples and counterexamples are presented.
