Yes, even though I like using JOINs, you can accomplish it without one. You'll need to change your query. This is how...
Example:
http://sqlfiddle.com/#!2/596b45/4 (MySQL 5.5)
http://sqlfiddle.com/#!3/bbad4/1 (SQL Server 2008)
http://sqlfiddle.com/#!12/bbad4/1 (PostgreSQL 9.2)
Assumption
1) In the employee table: manager id + department id will be unique
2) In the employee table: if employee Clark is ID 5 and has a manager with ID 1, there will a record in the table with ID 1
3) MySQL 5.5 is being used
Structure
create table dept
(
  dept_no int not null,
  dept_name varchar(100) not null,
  dept_location varchar(100) not null,
  primary key (dept_no)
);
create table employee 
(
  emp_id int not null,
  emp_name varchar(100) not null,
  mgr_emp_id int,
  dept_no int not null,
  primary key (emp_id),
  key employee_mgr_emp_id (mgr_emp_id),
  foreign key fk_employee_dept_dept_no (dept_no) references dept (dept_no) on delete no action on update no action
);
insert into dept values 
(1, 'Dept-1', 'Chicago'), 
(2, 'Dept-2', 'London');
insert into employee values 
(1, 'Clark Mgr', null, 1),
(2, 'Cameron Emp', 1, 1),
(3, 'Charlie Emp', 1, 1),
(4, 'Layton Emp', null, 2),
(5, 'Linda Emp', null, 2);
MySQL 5.5 query
Without JOIN
select 
  list.*,
  emp_id,
  emp_name
from employee, 
(
  select
    distinct 
    dept.dept_no, 
    dept.dept_name, 
    dept.dept_location, 
    employee.mgr_emp_id
  from dept, employee
  where 
    dept.dept_no = employee.dept_no
    and employee.mgr_emp_id is not null
) list
where
  employee.emp_id = list.mgr_emp_id;
With JOIN (although not completely identical to the above. I prefer using JOINs)
select 
  list.*,
  emp_id,
  emp_name
from employee
inner join 
(
  select
    distinct 
    dept.dept_no, 
    dept.dept_name, 
    dept.dept_location, 
    employee.mgr_emp_id
  from dept
  left join employee on dept.dept_no = employee.dept_no
  where 
    employee.mgr_emp_id is not null
) list
on employee.emp_id = list.mgr_emp_id;
How does it work
The first thing we need is a list of all the departments in the employee table with manager IDs that are not null. We use the following query to achieve that. Due to the existence of 2 records in the employee database with a valid manager ID for Chicago's department, this query returns 2 records for Chicago.
Without JOIN
select
  dept.dept_no,
  dept.dept_name,
  dept.dept_location,
  employee.mgr_emp_id
from dept, employee
where
    dept.dept_no = employee.dept_no
    and employee.mgr_emp_id is not null;
With JOIN
select
  dept.dept_no,
  dept.dept_name,
  dept.dept_location,
  employee.mgr_emp_id
from dept
left join employee on dept.dept_no = employee.dept_no
where
    employee.mgr_emp_id is not null;
To get only one record, we will use distinct keyword:
  select
    distinct 
    dept.dept_no, 
    ...
Great, so now we know who the manager is for each department no. Let's find this person's name. To do that, we put our query in a subquery (which I nicknamed/aliased as list) and then combine it with employee table to get the desired result.
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