A new method has been developed to combine unbiased sample data with possibly biased extra information. This method is similar to the James-Stein estimator and outperforms the sample mean in terms of accuracy. When the extra information is unbiased, the new method has slightly higher risk than the usual combined estimator. But as the bias in the extra information increases, the risk of the new method remains bounded while the usual estimator's risk becomes unbounded. The new method is like a best linear combination of sample data and extra information, can be seen as an empirical Bayes estimator, and can help in constructing confidence sets. In a study using real forestry data, the new method showed better performance compared to the sample mean and the usual combined estimator.