Help with Countif function (normal count unless another column states a certail text)

Hi all, 

I currently have a countif formula counting the number of projects staff members in my team are assigned to

=COUNTIF('Work-Database'!E:E,"*Staff Member Name*")

Ideally, I would like to add to this formula so that when column M states "Complete" this row/project isn't included in the count. I.e. were only counting live projects as opposed to completed projects.

Is this possible? Thanks in advance!