  We consider the problem of testing whether an unknown $n$-variable Boolean
function is a $k$-junta in the distribution-free property testing model, where
the distance between function is measured with respect to an arbitrary and
unknown probability distribution over $\{0,1\}^n$. Chen, Liu, Servedio, Sheng
and Xie showed that the distribution-free $k$-junta testing can be performed,
with one-sided error, by an adaptive algorithm that makes $\tilde
O(k^2)/\epsilon$ queries. In this paper, we give a simple two-sided error
adaptive algorithm that makes $\tilde O(k/\epsilon)$ queries.
