  Let C_1 and C_2 be algebraic plane curves in the complex plane such that the
curves intersect in d_1\cdot d_2 points where d_1,d_2 are the degrees of the
curves respectively. Oka and Sakamoto proved that the fundamental group of the
complement of C_1 \cup C_2 is isomorphic to the direct of product of the
fundamental group of the complement of C_1 and the fundamental group of the
complement of C_2. In this paper we prove the converse of Oka and Sakamoto's
result for line arrangements. Let A_1 and A_2 be non-empty arrangements of
lines in complex plane such that the fundamental group of the complement of A_1
\cup A_2 is isomorphic to the direct product of the complements of the
arrangements A_1 and A_2. Then, the intersection of A_1 and A_2 consists of
|A_1| \cdot |A_2| points of multiplicity two.
