In statistical literature, several methods are available to generate a new probability distribution by introducing new parameter to any existing standard distribution. The quadratic rank transmutation map method is one of these and received considerable attention in the literature. Here, we also proposed a new probability distribution using this method when DUSE (θ)-distribution is chosen as baseline distribution. The proposed distribution is called transmuted DUSE (θ)-distribution, which is seems to be more flexible as compared to the baseline distribution. Different statistical properties such as moments, quantile function, survival function, hazard function and order statistics have been derived. Also, the method of maximum likelihood and method of maximum product spacing are used to estimate the unknown parameters of the introduced probability distribution. Simulation study is being carried out to know the long-run behavior of the distribution. Finally, a real data set has been utilized to show the applicability of the proposed distribution.