multivariate regression

I would like to use a multivariate regressor of X to Y, while maintaining that the regression values are yet uncorrelated as possible to another variable Z? Y and Z maybe somewhat correlated.

X is n by k, Y is n by 1 and Z is n by 1. So basically we would like to have a multivariate regression technique for independent variable X to dependent variable Y, while minimizing the correlation (need not be 0) between the regression values and Z.

Could you kindly let me know if there any regression method which addresses this problem? It would be great if there is an R package for it?

Thanks a lot.