Rub the peel of the lime (it should make about 1 tablespoon of grated lime peel) and squeeze out the juice. Puree the bananas. Mix the lime juice and zest as well as the orange juice with the banana puree.
Pour everything into a large saucepan and mix in the preserving sugar. Bring to the boil while stirring and continue to cook for approx. 4 minutes, stirring constantly. Skim off the resulting foam. If you prefer jam with a bit of bite, you can mix in 2 - 3 tablespoons of desiccated coconut.
Put the jam almost full to the brim in prepared, i.e. rinsed, jars, close them and place on the lid for 5 - 10 minutes.