  Ruskey and Savage asked the following question: Does every matching of
$Q_{n}$ for $n\geq2$ extend to a Hamiltonian cycle of $Q_{n}$? J. Fink showed
that the question is true for every perfect matching, and solved the Kreweras'
conjecture. In this paper we consider the question in hypercubes with faulty
edges. We show that every matching $M$ of at most $2n-1$ edges can be extended
to a Hamiltonian cycle of $Q_{n}$ for $n\geq2$. Moreover, we can prove that
when $n\geq4$ and $M$ is nonempty this result still holds even if $Q_{n}$ has
at most $n-1-\lceil\frac{|M|}{2}\rceil$ faulty edges with one exception.
