If the table has more than two (including two) index, which has a unique index, and the other non-uniqueness.
In this case, ORACLE will use the unique index and completely ignore the non-uniqueness of the index.
For example:
SELECT ENAME
FROM EMP
WHERE EMPNO = 2326
AND DEPTNO = 20 ;
Here, only the index on the EMPNO is unique in nature, so EMPNO index will be used to retrieve records.
TABLE ACCESS BY ROWID ON EMP
INDEX UNIQUE SCAN ON EMP_NO_IDX