This is an announcement for the paper "L'Application canonique $J:H^2(X) \otimes H^2(X)->H^1(X\otimes X)$ n'est pas surjective en g\'en\'eral" by Omran Kouba. Abstract: We introduce the $H^1$-projective property, and use it to construct a Banach space $X$ such that the natural map $J:H^2(X)\otimes H^2(X) -> H^1(X\otimes X)$ is not onto. Archive classification: Functional Analysis Mathematics Subject Classification: 46M05;47A56;47A68 Citation: C.R. Acad. Sci. Paris t.307, Serie I, (1988), 949-953 Remarks: 9 pages, French with abridged english version The source file(s), ART1.Tex: 27483 bytes, is(are) stored in gzipped form as 0401335.gz with size 9kb. The corresponding postcript file has gzipped size 45kb. Submitted from: omran_kouba@hiast.edu.sy The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/math.FA/0401335 or http://arXiv.org/abs/math.FA/0401335 or by email in unzipped form by transmitting an empty message with subject line uget 0401335 or in gzipped form by using subject line get 0401335 to: math@arXiv.org.