A technique for computation of variances and covariances of normal order statistics is presented. This method provides the means to extend the precision of and correct errors in current tables. A numerical integration approach is employed for the calculations and associated error bounds are developed. Tables were constructed for samples sizes up to M with precision as follows: 25 decimal places (d.p.) for samples sizes of 2(1)20; 20 d.p. for 21(1)30; 15 d.p. for 31(1)40; 10 d.p. for 41(1)50. A table of variances and covariances for sample sizes up to 20 and a table of product moments of normal order statistics for samples sizes of 20(10)50 are presented.