Makespan minimisation of permutation flowshop scheduling problems (PFSP) with sequence dependent setup times (SDST) is NP-Hard. PFSP-SDST has important practical applications e.g. in the paint industry. There exist several algorithms for PFSP-SDST, but they just use generic methods that lack specific structural information of the problem and so struggle with large-sized problems or find low quality solutions. In this paper, we propose a constraint-directed local search (CDLS) algorithm, which takes SDST constraints into account. SDSTs cause delays in job processing and directly affect the makespan. The PFSP-SDST solving algorithms should therefore explicitly incorporate these constraints in their search decisions. In this paper, we define a measurement of delays created by SDST constraints. The CDLS algorithm then gives priorities to the jobs that cause the highest delays since these jobs are in the most problematic parts of the solution. Our experimental results on 220 well-known instances show that the CDLS algorithm significantly outperforms the existing state-of-the-art algorithms. Moreover, it obtains new upper bounds for 163 instances out of those 220.