  We generalize the Bartsch-Li's splitting lemma at infinity for
$C^2$-functionals in [2] and some later variants of it to a class of
continuously directional differentiable functionals on Hilbert spaces.
Different from the previous flow methods our proof is to combine the ideas of
the Morse-Palais lemma due to Duc-Hung-Khai [9] with some techniques from [11],
[17], [18]. A simple application is also presented.
