If you have a primary key field--a field with a unique value in every record, include it as an additional match field, but use the ≠ operator instead of =. You can double click the relationship line to pull up a dialog where you can make this change.
In that dialog, the relationship match fields will look similar to this:
Table::OrganizationID = Table 2::OrganizationID AND
Table::PrimaryKey ≠ Table 2::PrimaryKey