Search for line containing stringB, not preceded by a line containing stringA

I have a text file and I would like to compose a regular expression
that matches lines containing stringB but not preceded by a line
containing string A. I thought one of these might do it:

\(stringA.*\n\)\@<!.*stringB
\(stringA.*\n\)\@<!\(.*stringB\)

The \@<! was *intended* to ensure a non-match with stringA in the
preceding line. However, they highlight the same lines that are
highlighted by the opposite regular expressions:

\(stringA.*\n\)\@<=.*stringB
\(stringA.*\n\)\@<=\(.*stringB\)

With a little pondering, it is obvious why. The first .* matches any
set of characters, so even if stringA exists in the preceding line,
you can always find some portion of the line that doesn't match
\(stringA.*\n\).

Is there a way to achieve the search described in above?

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