Plagiarism is a widely spread problem that is the main focus of interest these days. In this paper, we propose a new method solving associations of phrases contained in text documents. This method, called SVDPlag, employs Singular Value Decomposition (SVD) for this purpose. Further, we discuss other approaches to plagiarism detection and compare them with our method. To examine the efficiency of plagiarism detection methods, we used an experimental corpus of 950 text documents about politics, which were created from the standard CTK corpus. The experiments indicate that our approach significantly improves the accuracy of plagiarism detection and overcomes other methods.