  For a double complex $(A, d', d'')$, we show that if it satisfies the
$d'd''$-lemma and the spectral sequence $\{E^{p, q}_r\}$ induced by $A$ does
not degenerate at $E_0$, then it degenerates at $E_1$. We apply this result to
prove the degeneration at $E_1$ of a Hodge-de Rham spectral sequence on compact
bi-generalized Hermitian manifolds that satisfy a version of $d'd''$-lemma.
