Logic Built-In Self Test (LBIST) is a popular technique for applications requiring in-field testing of digital circuits. LBIST incorporates test generation and response-capture on-chip. It requires no interaction with a large, expensive tester. LBIST offers test time reduction due to at-speed test pattern application, makes possible test data re-usability at many levels, and enables test-ready IP. However, the traditional pseudo-random pattern-based LBIST often has a low test coverage. This paper presents a new method for on-chip generation of deterministic test patterns based on registers with non-linear update. Our experimental results on 7 real designs show that the presented approach can achieve a higher stuck-at coverage than the test point insertion with less area overhead. We also show that registers with non-linear update are asymptotically smaller than memories required to store the same test patterns in a compressed form.