A process wherein substrate preliminary formed with bumps by electrolytic plating or other technique is prepared. The semiconductor device is opposed to the substrate with the bumps so that the Al electrodes of the semiconductor device are aligned with respect to the bumps and brought into contact with each other. Then, the Al electrodes of the semiconductor device and the bumps are bonded together by the application of pressure and heat with an Au--Al alloy layer formed therebetween. Subsequently, the bumps are peeled off the substrate so as to be transferred to the respective Al electrodes. Thereafter, the semiconductor device is opposed to a circuit board so that the bumps are aligned with respect to the electrodes of wiring and brought into contact with them. Then, the bumps and the electrodes of wiring are bonded together more securely by the application of a larger pressure at a higher temperature or by the application of pressure and heat for a longer period of time than in the preceding process with another Au--Al alloy layer newly formed therebetween to cover a wider range. Thereafter, the bumps and electrodes of wiring are fixed and connected by means of a photo-curing insulating resin. Thus, the bonds between the Al electrodes and the bumps are strengthened while preventing the considerable deformation of the bumps before they are connected to the electrodes of wiring. According to the connecting method, connecting reliability is greatly improved when the transfer method whereby the bumps are easily formed on the electrodes of the semiconductor device at low cost is applied to the flip flop method or to the MBB method.