Randomizer with out duplicates

Is there a formula that I can put into a range of cells that will populate the cells with random names from a list...without duplicates?

For example I have a list in A1- A16. I then have =RAND() in C1 - C16. I then have =INDEX(A:A,COUNTA(A:A)-RANK(C1,C:C)) in D1-D16. With C1 ascending accordingly.

Lastly, I have a macro in a form of button with the following code.

Sub Randomize()
'
' Randomize Macro
'
'

'
Calculate
End Sub

Thanks so much in advance!

Thank you very much martindwilson. And thank you for the quick response.