In this paper, we develop the noninformative priors for the ratio of the scale parameters in the inverted exponential distributions. The first and second order matching priors, the reference prior and Jeffreys prior are developed. It turns out that the second order matching prior matches the alternative coverage probabilities, is a cumulative distribution function matching prior and is a highest posterior density matching prior. In addition, the reference prior and Jeffreys` prior are the second order matching prior. We show that the proposed reference prior matches the target coverage probabilities in a frequentist sense through a simulation study as well as provide an example based on real data is given.