The cycle of heat engine which produces the maximum power output is constructed when heat sources are finitely constant, and the maximum power as a thermodynamic limit of the engine, is obtained. The characteristics of the maximum power cycle are as follows, which represent the operation conditions and design conditions of the heat engine to produce the maximum power output. In heat exchangers, the temperature profiles of the heat source and the working fluid have the same functional formula and the ratio of the working fluid temperature to the heat source temperature is constant. When heat capacity flow rates(product of the specific heat and the mass flow rate) of the working fluid as well as the heat source are constant, the values of those of working fluid exist between those of two heat sources. The relation of the temperature and the heat capacity flow rate is established without the states of the heat sources and the capacities of heat exchangers, which is ( $T_{h}$/ $T_{H}$)( $C_{h}$/ $C_{H}$)=( $T_{1}$/ $T_{L}$)( $c_{1}$/ $c_{L}$)=1. The capacity of the heat exchanger of hot side is equal to that of cold side regardless of the states of the heat sources and the total capacities of heat exchangers.hangers.ers.