  We study the free path problem, i.e., if we are given two free arrangements
of hyperplanes, then we can connect them by free arrangements or not. We prove
that if an arrangement $\mathcal{A}$ and $\mathcal{A} \setminus \{H,L\}$ are
free, then at least one of two among them is free. When $\mathcal{A}$ is in the
three dimensional arrangement, we show a stronger statement.
