  In this paper we prove that there exists a function which $f(x)$ belongs to
$L^1[0,1]$ such that a greedy algorithm with regard to the Walsh subsystem does
not converge to $f(x)$ in $L^1[0,1]$ norm, i.e. the Walsh subsystem
$\{W_{n_k}\}$ is not a quasi-greedy basis in its linear span in $L^1$.
