Our reader Andrea (andrea[dot]perugia[-at-]gmail[dot] com) sent his circuit to us, and he creates the circuit for educational intent. The main purpose is to show that you can toggle an output state electronically, although physically you use only a push button switch. Here is what he said about the cicuit :

This simple circuit can be utilized to drive a monostable relay, using a single button switch. When I press the button IC output (pin 3) assumes the high level, but Q1 transistor switches off. So when I release the button the relay is energized (now the exchange switch is closed on 5 and 9). When I press the button again IC output assumes the low level, but Q3 transistor switches on:
when I release the button the circuit goes to the start condition.

Here is the schematic diagram of the circuit:

alternating relay switch circuit schematic