An oilless high pressure pump suitable for use in devices such as pressure washers and the like is described. The pump includes an eccentric assembly suitable for converting rotary motion of a rotating shaft to rectilinear motion. One or more straps couple the eccentric assembly to the pump's piston assembly. The straps communicate the rectilinear motion of the eccentric assembly to the piston assembly for reciprocating the pump's pistons to pump the liquid.