Traditional blockchain systems, such as Bitcoin, focus on transactions in which entire amount is transferred from one owner to the other, in a single, atomic operation. This model has been re-used in the context of payment networks such as Lightning network. In this work, we propose and investigate new payment model, called split payments, in which the total amount to be transferred is split into unit-amounts and is transferred independently through the same or different routes. By splitting the payments this way, we achieve an improved total liquidity of the payment network, simplify the route advertising, reduce the amount of funds needed to be locked in the channels, and improve the privacy properties.