A die mounting system comprising: a die supply device that supplies dies formed from a single diced wafer affixed to a dicing sheet and that is set on a component mounter, the die supply device including a supply head that picks up a die from the dicing sheet and is then vertically inverted, and a supply head moving mechanism that moves the supply head; a mounting head of the component mounter that picks up a die supplied from the die supply device and mounts the die on a circuit board; and a control system that controls operation such that the supply head is moved above the die which is to be the pickup target by the supply head moving mechanism, the die is picked up by the supply head, the supply head is vertically inverted, the supply head is moved to a die transfer position by the supply head moving mechanism, and the die held by the supply head is picked up by the mounting head of the component mounter at the transfer position and mounted on a circuit board, wherein the control system sets a next die transfer position such that cycle time is shortened by the longer of two times being made shorter and the time difference of the two times being made smaller, the two times being the time required, after the completion of die transfer operation of picking up a die held by the supply head of the die supply device with the mounting head of the component mounter at the die transfer position, for die transfer preparation operation of inverting the supply head of the die supply device to its original state and moving the supply head above a die which is to be a pickup target, picking up the die, vertically inverting again, and moving to the next die transfer position, and the time required, after the completion of die transfer operation, for die mounting operation of moving the mounting head of the component mounter above the die mounting position on the circuit board, mounting the die on the circuit board, and moving the mounting head to the next die transfer position. a die supply device that supplies dies formed from a single diced wafer affixed to a dicing sheet and that is set on a component mounter, the die supply device including a supply head that picks up a die from the dicing sheet and is then vertically inverted, and a supply head moving mechanism that moves the supply head; a mounting head of the component mounter that picks up a die supplied from the die supply device and mounts the die on a circuit board; and a control system that controls operation such that the supply head is moved above the die which is to be the pickup target by the supply head moving mechanism, the die is picked up by the supply head, the supply head is vertically inverted, the supply head is moved to a die transfer position by the supply head moving mechanism, and the die held by the supply head is picked up by the mounting head of the component mounter at the transfer position and mounted on a circuit board, wherein the control system sets a next die transfer position such that cycle time is shortened by the longer of two times being made shorter and the time difference of the two times being made smaller, the two times being the time required, after the completion of die transfer operation of picking up a die held by the supply head of the die supply device with the mounting head of the component mounter at the die transfer position, for die transfer preparation operation of inverting the supply head of the die supply device to its original state and moving the supply head above a die which is to be a pickup target, picking up the die, vertically inverting again, and moving to the next die transfer position, and the time required, after the completion of die transfer operation, for die mounting operation of moving the mounting head of the component mounter above the die mounting position on the circuit board, mounting the die on the circuit board, and moving the mounting head to the next die transfer position.