The new system, which started last Monday, means all homes in the city which have individual wheelie bins will now have their green domestic waste bins and brown garden waste bins picked up on the same day on alternate weeks.
Grey food waste recycling bins will continue to be picked up weekly.
The council says food accounts for around a third of rubbish in an average bin, so the food recycling collections should mean less general rubbish is going out in the green wheelie bins.
An average of about 0.5 tonnes of rubbish is sent to landfill each year per household, which is seen as being harmful to the environment.
Edinburgh already recycles about a third of its waste, but national targets require that figure to rise to 50 per cent by 2014 and 70 per cent by 2025.