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For two normal populations with unknown means μ and unknown vari-ances σ2, assume that there are simple order restrictions among the means and vari-ances: μ1 ≤μ2 and σ12 ≥σ22 ＞ 0. This case is said to be simultaneous order re-striction by Shi (Maximum likelihood estimation of means and variances from normalpopulations under simultaneous order restrictions, J. Multivariate Anal., 50(1994),282-293.) and an iterative algorithm of computing the order restricted maximumlikelihood estimates ofμi and σi was given in that paper. This paper shows that therestricted maximum likelihood estimate ofμi has smaller mean square loss than theusual estimate xi under some conditions.