Unwanted lines in tables

I have a rather long table in landscape, spread over three pages. The first
column lists the subject, the second the organization, the third the
organization's convention and so on. Sometimes headings in the first and
second columns go over a page. The table does not have a visible grid, but I
have drawn lines under and above the first heading to make it clearer. But
for some reason, a line appears in the second column at the start of a page
although the cell is supposed to be a continuation from the next page (and
therefore should not have a line). I have tried erasing it and drawing it
with a "no border" setting, but I can't get it to go away.

I've tried to explain this the best I could. It's driving me nuts, and I
need to get the publication to print! Please help.

Suroor