Take a look at this :
Sub test_IngaB()
Dim FirstAddress As String, cF As Range, LookForString As String
LookForString = "Cat"
With ThisWorkBook.Sheets("Sheet's name").Range("F:F")
.Cells(1,1).Activate
'First, define properly the Find method
Set cF = .Find(What:=LookForString, _
After:=ActiveCell, _
LookIn:=xlFormulas, _
LookAt:=xlPart, _
SearchOrder:=xlByColumns, _
SearchDirection:=xlNext, _
MatchCase:=False, _
SearchFormat:=False)
'If there is a result, keep looking with FindNext method
If Not cF Is Nothing Then
FirstAddress = cF.Address
Do
cF.Offset(0, 3).Value = 1
Set cF = .FindNext(cF)
'Look until you find again the first result
Loop While Not cF Is Nothing And cF.Address <> FirstAddress
End If
End With
End Sub