Match 2 people together from list randomly using one condition

I am creating an excel sheet to randomly match 2 employees together from a list. Only criteria is that the employees cannot be apart of the same department.

I've created a formula that randomly matches people from a list, but have not been able to only match people if they are in different departments.

=INDEX($A:$A,RANDBETWEEN(1,COUNTA($A:$A)),1)

I expect the output to be: "John Doe IT" "Noah Body HR"

the current function can output: "John Doe IT" "Jane Doe IT"