Displaying The Maximum Value For Each Row Of Data

I have some code and it's not quite working.

For each row of data in my table (each row of data is contained in columns D:F) I want to display the maximum value in column H, of the same row. For some reason though it is putting it in 21 additional rows down.

Sub Winner()
Dim lngMax As Long
Dim lngRowLast As Long
Dim rng As Range
Dim rngAll As Range
Dim rngRow As Range
lngRowLast = Range("D65536").End(xlUp).Row
Set rngAll = Range("D2" & lngRowLast)
For Each rng In rngAll
Set rngRow = Range(rng, rng.Offset(0, 2))
lngMax = Application.WorksheetFunction.Max(rngRow)
rng.Offset(0, 4).Value = lngMax
Next rng
End Sub