This is easily solvable with analytic functions.  As you can see, there are two employees earning the maximum salary in DEPT 20; this is an important detail, as some common solutions to this kind of problem miss that information.  
SQL> select ename
  2             , deptno
  3             , sal
  4  from (
  5      select ename
  6             , deptno
  7             , sal
  8             , max (sal) over (partition by deptno) max_sal
  9             , min (sal) over (partition by deptno) min_sal
 10      from emp
 11      )
 12  where sal = max_sal
 13  or    sal = min_sal
 14  order by deptno, sal
 15  /
ENAME          DEPTNO        SAL
---------- ---------- ----------
KISHORE            10       1300
SCHNEIDER          10       5000
CLARKE             20        800
RIGBY              20       3000
GASPAROTTO         20       3000
HALL               30        950
LIRA               30       3750
TRICHLER           50       3500
FEUERSTEIN         50       4500
9 rows selected.
SQL>
Oops, I missed an important detail about the result format.  My data won't fit the requested output, because there are two employees earning the maximum salary.   So this query, which I admit is a bit awkward, gives us the required layout.  The MIN() on the employee names returns the alphabetical order : 
SQL> select
  2         deptno
  3         , max (case when sal = min_sal then min_sal else null end ) as min_sal
  4         , min (case when sal = min_sal then ename else null end ) as min_name
  5         , max (case when sal = max_sal then max_sal else null end ) as max_sal
  6         , min (case when sal = max_sal then ename else null end ) as max_name
  7  from (
  8      select ename
  9             , deptno
 10             , sal
 11             , max (sal) over (partition by deptno) max_sal
 12             , min (sal) over (partition by deptno) min_sal
 13      from emp
 14      )
 15  where sal = max_sal
 16  or    sal = min_sal
 17  group by deptno
 18  order by deptno
 19  /
    DEPTNO    MIN_SAL MIN_NAME      MAX_SAL MAX_NAME
---------- ---------- ---------- ---------- ----------
        10       1300 KISHORE          5000 SCHNEIDER
        20        800 CLARKE           3000 GASPAROTTO
        30        950 HALL             3750 LIRA
        50       3500 TRICHLER         4500 FEUERSTEIN
SQL>
I don't like this solution.  Most datasets will contain such clashes, and we need to acknowledge them.  Filtering the result on the basis of some unrelated criteria to fit a Procrustean report layout is misleading.  I would prefer a report layout which reflected the whole dataset.  Ultimately it depends on the business purpose which the query serves. And, of course, the customer is always right 8-)