We prove the existence of equilibrium in a simple exchange model. We assume that the excess demand function generated by the model under scrutiny is continuous and defined on open unit simplex of prices, satisfies Walras’ law and is bounded from below. We present a simple combinatorial lemma which is then used to prove the existence of zeros of the excess demand function. There is no reference to Brouwer’s fixed point theorem which is standard tool while proving the existence of equilibrium. Our approach allows to compute approximate equilibrium in – as we believe – a novel way.