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We submit a new way to detect pairs of non-cobordant surface-links. We find anew example of a pair of non-cobordant surface-links with the followingproperties: Orr invariant, Cochran sequence, Sato-Levine invariant, thealinking number and one of Stallings's theorems cannot distinguish them.However our new way can distinguish them.

A new pair of non-cobordant surface-links which the Orr invariant, the  Cochran sequence, the Sato-Levine invariant, and the alinking number cannot  find