This paper describes the implementation of a second-order hidden Markov model (HMM) based part-of-speech tagger for the Apertium free/opensource rule-based machine translation platform. We describe the part-ofspeech (PoS) tagging approach in Apertium and how it is parametrised through a tagger definition file that defines: (1) the set of tags to be used and (2) constrain rules that can be used to forbid certain PoS tag sequences, thus refining the HMM parameters and increasing its tagging accuracy. The paper also reviews the Baum-Welch algorithm used to estimate the HMM parameters and compares the tagging accuracy achieved with that achieved by the original, first-order HMM-based PoS tagger in Apertium.