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Weighted regression in REML

Hello:
I'm reading the book of Searle:
http://www.leg.ufpr.br/~eder/Variance%20Components.pdf

I think that equation 53 on p 276 suggests that if one wants to use weights in REML, the solution is very similar to that in OLS: multiply X, Z, and Y by the square root of the weight matrixand proceed as in unweighted case. Am I right or there is more that needs to be done?
Regards,Nik