This is an announcement for the paper "Non-intersection bodies all of whose central sections are intersection bodies" by M.Yaskina. Abstract: We construct symmetric convex bodies that are not intersection bodies, but all of their central hyperplane sections are intersection bodies. This result extends the studies by Weil in the case of zonoids and by Neyman in the case of subspaces of $L_p$. Archive classification: Functional Analysis; Metric Geometry Mathematics Subject Classification: 52A20, 52A21, 46B20 Remarks: 10 pages The source file(s), inters8.tex: 33376 bytes, is(are) stored in gzipped form as 0505277.gz with size 10kb. The corresponding postcript file has gzipped size 54kb. Submitted from: yaskinv@math.missouri.edu The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/math.FA/0505277 or http://arXiv.org/abs/math.FA/0505277 or by email in unzipped form by transmitting an empty message with subject line uget 0505277 or in gzipped form by using subject line get 0505277 to: math@arXiv.org.