  After the solution of Cousin II problem by K. Oka III in 1939, he thought an
{\it extra-zero problem} in 1945 (his posthumous paper) asking if it is
possible to solve an arbitrarily given Cousin II problem adding some
extra-zeros whose support is disjoint from the given one. By the secondly named
author, some special case was affirmatively confirmed in dimension two and a
counter-example in dimension three or more was given. The purpose of the
present paper is to give a complete solution of this problem with examples and
to discuss some new questions.
