Double negation

Unless she is in a meeting and cannot be interrupted, the director would like to be notified when an important client arrives.

"Unless" "cannot be"
I think this is a double negation, whih is not a very good way to write.

Am I right on this or wrong?
Please help me with this.
Thanks.

'Double negation' has two different meanings. Your example is a negation of a negation. This is quite all right; it is standard English, and it is easy enough to understand. 'Unless she cannot be interrupted' = 'if she can be interrupted'.

There are some dialects of English that mark a single negation in two places in a sentence. For example, 'I did see thing.' This is one negation of the statement 'I saw something.' But the standard dialect does not say this, so you should not say this. (Though you should understand and accept it: it is very common.)