How can I conditionally format a cell based on the value in a different cell.

I have two columns of information. None of the information in the cells I am
trying to format is numeric. I am trying to track names to loans that are
with the company. If they wrote outside, I need to keep track of which other
company it was written with.

The First column currently has a conditional format to highlight the cell if
the value is = "Home". The other values that are entered are variations of
"Outside". I have to keep the variations as they are, in order to track which
loans went with which other company.

The second column has the borrowers name. I need this column to highlight
the cells if the loan was written outside.

So if the cell is highlighted in column A, it should not be highlighted in
the column B.
And Vice versa.