A two-step procedure is given to find the sample size necessary to estimate the parameter θ in the uniform density withindunits of the true value. It is demonstrated that an exact solution for all values of θ doesn't exist based on the maximum likelihood estimator. A table is presented which can be used to find the second sample size,n, such thatP[|yn− θ| <d] > 1− α is true, whereYnis the largest observation in the second sample, for 1 − α = .90, .95, .99 and the preliminary sample sizem= 2, 5 (5) 30 (10) 50 (25) 100. Also a table of comparisons between the expected sample size in this paper and two other solutions is given.