  Recently, there has been a lot of work on constructions of permutation
polynomials of the form $(x^{2^m}+x+\delta)^{s}+x$ over the finite field
$\F_{2^{2m}}$, especially in the case when $s$ is of the form $s=i(2^m-1)+1$
(Niho exponent). In this paper, we further investigate permutation polynomials
with this form. Instead of seeking for sporadic constructions of the parameter
$i$, we give a general sufficient condition on $i$ such that
$(x^{2^m}+x+\delta)^{i(2^m-1)+1}+x$ permutes $\F_{2^{2m}}$, that is, $(2^k+1)i
\equiv 1 ~\textrm{or}~ 2^k~(\textrm{mod}~ 2^m+1)$, where $1 \leq k \leq m-1$ is
any integer. This generalizes a recent result obtained by Gupta and Sharma who
actually dealt with the case $k=2$. It turns out that most of previous
constructions of the parameter $i$ are covered by our result, and it yields
many new classes of permutation polynomials as well.
