This paper presents a seamless algorithm for the application of the multilevel Monte
Carlo (MLMC) method to the ensemble transform particle filter (ETPF). The algorithm uses a combi-
nation of optimal coupling transformations between coarse and fine ensembles in difference estimators
within a multilevel framework, to minimise estimator variance. It differs from that of Gregory et al.
(2016) in that strong coupling between the coarse and fine ensembles is seamlessly maintained during
all stages of the assimilation algorithm, instead of using independent transformations to equal weights
followed by recoupling with an assignment problem. This modification is found to lead to an increased
rate in variance decay between coarse and fine ensembles with level in the hierarchy, a key component
of MLMC. This offers the potential for greater computational cost reductions. This is shown, alongside
evidence of asymptotic consistency, in numerical examples.