We improve two families of unbiased estimators in general form for estimating the finite population mean in stratified random sampling. These estimators are developed from the unbiased formal for two families of estimators given by Koyuncu and Kadilar (2009). We compute the variance equations of the suggested families of estimators. These equations are compared with the minumum cases of the mean squared errors (MSE) proposed by Koyuncu and Kadilar (2009). The fact that the minimum variance values of the suggested estimators are smaller than the minimum MSE values of estimators given in Koyuncu and Kadilar (2009) under the obtained conditions, is also shown by both theoretical comparisons and a numerical example.