We show, first, that the normalization procedure for S4 modal logic presented by Dag Prawitz in  does not work. We then develop a new natural deduction system for S4 classical modal logic that is logically equivalent to that of Prawitz, and we show that every derivation in this new system can be transformed into a normal derivation.
"A new S4 classical modal logic in natural deduction." J. Symbolic Logic 71 (3) 799 - 809, September 2006. https://doi.org/10.2178/jsl/1154698578