MOTIVATION: Over the past 30 years, extended tandem repeats (TRs) have been correlated with ∼60 diseases with high odds ratios, and most known TRs consist of single repeat units. However, in the last few years, mosaic TRs composed of different units have been found to be associated with several brain disorders by long-read sequencing techniques. Mosaic TRs are difficult-to-characterize sequence configurations that are usually confirmed by manual inspection. Widely used tools are not designed to solve the mosaic TR problem and often fail to properly decompose mosaic TRs. RESULTS: We propose an efficient algorithm that can decompose mosaic TRs in the input string with high sensitivity. Using synthetic benchmark data, we demonstrate that our program named uTR outperforms TRF and RepeatMasker in terms of prediction accuracy, this is especially true when mosaic TRs are more complex, and uTR is faster than TRF and RepeatMasker in most cases. AVAILABILITY AND IMPLEMENTATION: The software program uTR that implements the proposed algorithm is available at https://github.com/morisUtokyo/uTR.