Andrzej Kielbasinski, Krystyna Zietak,
 
Note on ``A new scaling for Newton's iteration 
for the polar decomposition and it's backward stability"
by R. Byers and H. Xu"


We show that the proof of Theorem 4.5 in the paper by Byers and Xu
is not complete for the considered class of matrices. The first order
analysis is not applicable to the considered problem of rounding error 
propagation. 

key words:  polar decomposition, Newton's method, backward stability