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In the paper, we construct a more precise prediction interval of the jth order observation from some pivotal quantities for the one-parameter exponential distribution based on Type II censored samples. Our method is more general in the sense that it can be applied to any data scheme. From the illustrated examples and the results of simulation, the performances of our method are better than the widely-used methods of Mann and Grubbs [12] and Kaminsky and Nelson [5,6]. For further study, our method is easily applied to other location and scale family distributions.