You'd need to modify your relationship so that no fields specified are empty. A calculation field could be used in place of a field that may be empty with code such as:
If ( IsEmpty (fieldthatMaybeEmpty ) ; "ZZZZZZZZZZZZZZZ" ; fieldthatMaybeEmpty )
Then use it in your relationship.
But if your goal is to prevent creating a record where the data in these fields are duplicated, you don't need a relationship to do so.
Define a text field with a calculation such as:
Field1 & "|" & Field2 & "|" & Field3 & ..... //include all fields that you currently use in your relationship.
Then specify a unique values validation on this new field and you'll get an error message and an option to either edit the values or revert the record each time a user attempts to create a records where the data in these fields match an existing record.
Excellent! Thanks again for your help and quick response.