Msgbox Won't Disappear When Opening Inputbox

I've created some code so that when users want to update something on and Excel template I'm creating for them that the information they've put in is backed up. They give the backup a name using an inputbox and it loops through previously loaded backups that I've stored in a separate sheet and checks if the backup already exists. If it does a msgbox appears to ask them if they want to replace the existing copy. If they choose not to, it re-opens the inputbox.

The issue I'm having is that the msgbox doesn't close before the input box opens and it looks messy and may be confusing. Is there any way, without creating a useform, that I can force the msgbox to close once the user has made a choice before the inputbox opens?

Here is the code:

Code:
1
BackName = InputBox("Give the backup a name", "Backup Name")
If BackName = "" Then GoTo 2

For i = 1 To LR1
If UCase(Sheet18.Cells(i, 1).Value) = UCase(BackName) Then
If MsgBox("Backup already exists. Replace?", vbYesNo) = vbYes Then

[Code] ......