Linear transformations preserving best linear unbiased estimators in a general Gauss-Markoff model

Under a general Gauss-Markoff model {y,X,β,V}, a necessary and sufficient condition is established for a linear transformation, F, of the observable random vector y to have the property that there exists a linear function of Fy which is a BLUE of Xβ. A method for deriving a required BLUE from the transformed model {Fy,FXβ,FVF′} is also indicated.