<p>Recently, randomized algorithms have gained considerable attention as efficient techniques for dimension reduction in large-scale data across various scientific fields. In this paper, we introduce a randomized algorithm for third-order tensor decomposition based on the tensor-tensor product (t-product) using a unitary transform. Our approach is motivated by randomized tensor approximation methods that depend on random projections of each frontal slice of a tensor. However, these methods still incur high computational costs when applying SVD or column-pivoted QR decomposition to the slices. To improve the efficiency of randomized algorithms, we propose a randomized tensor QLP decomposition (rt-QLP) for third-order tensors without pivoting, extending the matrix-based QLP to the tensor setting in the transformed domain. Deterministic and probabilistic error bounds are derived by combining properties of the t-product with existing error analysis results of matrix QLP. The effectiveness and efficiency of the proposed method are demonstrated through extensive numerical experiments on tasks such as data compression, image completion, and facial recognition.</p>