Many Built-In Self Test pattern generators use Linear Feedback Shift Registers (LFSR) to generate test sequences. In this paper, we address the generation of deterministic pairs of patterns for delay faults testing with LFSRs. A new synthesis procedure for a n-sizeLFSR is given and guarantees that a deterministic set of n precomputed test pairs is embedded in the maximal length pseudo-random test sequence of the LFSR. Sufficient and necessary conditions for the synthesis of this pseudodeterministic LFSR are provided and show that at-speed delay faults testing becomes a reality without any additional cost for the LFSR. Moreover, since the theoretical properties of LFSRs are preserved, our method could be beneficially used in conjunction with any other technique proposed so far.