Tables :: Prohibiting Duplicate Data In A Table

I'm having some issues with stopping duplicate entries in a table and have tried a copule different ways with no avail.

In one table in particular, I have a table holding employees as followed;

EmployeeID: PK
FirstName
MInitial
LastName
Company:FK
DepartmentFK

What I am trying to do is stop the ability to duplicating records over a series of fields (FirstName, MInitial, LastName, Company)rather than just one specific field.

I attempted to index the table as followed;

EmployeeID: PK/Unique
FirstName: Unique
MInitial: Unique
LastName: Unique
Company: Unique

The problem with this is it wont allow me to enter more than one person with the same first, middle, or last name or company.

I tried "DCount" Code in a form with no luck, that code reads as followed:

Code:
Private Sub Form_BeforeUpdate(Cancel As Integer)
If DCount("*", "tblEmployees", "[firstname]=" & Chr(34) & Me!firstname & Chr(34) & _
" And [MInitial]=" & Chr(34) & Me!MInitial & Chr(34) & _
" And [LastName]=" & Chr(34) & Me!LastName & "#") > 0 Then
Msgbox "Person already exists."
Cancel = True
End If
End Sub

Note: this code was initially used on a different database I was working on that accounted for an individuals First Name, Last Name, and Date of Birth which worked great. I am just trying to apply that similar concept to this new database with first name, middle initial, last name, and company; which will be a foreign key.