Preheat oven to 350 degrees. Line a loaf pan with parchment paper.
Combine flour, baking powder, soda, and salt and sift together.
In a separate, slightly larger bowl cream the butter until light and fluffy. Add sugar to the butter and blend with mixer until well blended and smooth.
Beat eggs in a small bowl or cup and add to the butter mixture. Mix until well blended.
Mash the ripened bananas and then fold into the egg and sugar mixture and mix with a fork or whisk until well blended. You don't want to over mix this part.
Fold flour mixture into the wet mixture in four separate portions and mix well after each addition.
Once blended well you can turn the ingredients into parchment paper-lined loaf pan.
Bake for about 50 minutes or until it is golden brown. You should be able to insert a fork or toothpick and it remains dry. Once cooled slightly you can lift the loaf right out of loaf pan with parchment paper and place on a rack to cool. Once cooled, wrap tightly with plastic or foil to keep fresh and moist.