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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 ispossible to solve an arbitrarily given Cousin II problem adding someextra-zeros whose support is disjoint from the given one. By the secondly namedauthor, some special case was affirmatively confirmed in dimension two and acounter-example in dimension three or more was given. The purpose of thepresent paper is to give a complete solution of this problem with examples andto discuss some new questions.

On Oka's Extra-Zero Problem