The key ideas behind most of the recently proposed Markov networks based EDAs were to factorise the joint probability distribution in terms of the cliques in the undirected graph. As such, they made use of the global Markov property of the Markov network. Here we presents a Markov Network based EDA that exploits Gibbs sampling to sample from the Local Markov property, the Markovianity, and does not directly model the joint distribution. We call it Markovianity based Optimisation Algorithm. Some initial results on the performance of the proposed algorithm shows that it compares well with other Bayesian network based EDAs. Categories and Subject Descriptors I.2.8 [Artificial Intelligence]: Problem Solving, Control Methods, and Search ; G.3 [Probability and statistics]: Probabilistic algorithms, Stochastic processes General Terms Algorithms, Performance, Design Keywords Estimation of Distribution Algorithms, Probabilistic graphical models, Markov Networks, Evolutionary Computation