There exists a Gödel number for each formula of the system N of natural numbers. The Gödel undecidable proposition, which is also a formula of the system N, also exists a Gödel number p; at the same time, the Gödel undecidable proposition is a self-referential proposition u([p]) substituted into its own Gödel number, and the self-referential proposition u([p]) Gödel number is also p, i.e., there is, u([p])=p. It can be This equation has no solution.The traditional view is that the Gödel undecidable proposition u([p]) is a closed formula and is a natural number proposition; we here transform the Gödel self-referential proposition into a self-referential equation and find that this equation has no solution and the Gödel undecidable proposition u([p]) is not a natural number proposition. u([p]) is an unclosed term (out-of-domain term) that evolves on the set of natural numbers and u([p]) is not a closed formula.