Heat oven to 350°F. Grease a Bundt pan or two 9"x5"x3" loaf pans.
Sift flour, baking powder, soda, salt. With electric mixer at medium speed, thoroughly mix shortening with sugar, then eggs, until very light and fluffy, about 4 minutes. Then, at low speed, beat in flour mixture alternately with bananas just until smooth; turn into pan.
Bake 50 minutes to 1 hour, or until a toothpick inserted into the center comes out clean. Cool in pan 10 minutes; remove. Cool before slicing.
Recipe adapted from Good Housekeeping Cook Book, 1942.