We study the problem of allocating a set of m indivisible goods among n agents with additive valuations in a fair manner using the popular fairness notion of Maximin share (MMS). Maximin share of agent i (MMS_i) is the maximum value she can guarantee to have assuming that she divides the goods into n bundles and gets the minimum valued bundle. An alpha-MMS allocation is an allocation which gives all agents alpha times their Maximin share. It is known that 1-MMS allocations do not always exist and 3/4-MMS allocations always exist. Yet this factor has not been improved (by an additive constant) since the work of Ghodsi et al. in 2018. We improve the state-of-the-art by showing that (3/4+3/4220)-MMS allocations always exist.