Prevent Conditional Formatting on Blank Cells

I want to highlight identical entries between two columns, using conditional formatting on the first column, but if the entry in both columns is blank, I don't want the cell highlighted. I tried using

=NOT(ISBLANK(A1))=NOT(ISBLANK(C1))

but this doesn't prevent blank matches from being highlighted, is there any wayto do this? I've attached a quick sample. In the sample I wouldn't want cell A6 to be highlighted because both A6 and C6 are blank.

Many thanks