The cover of Action Comics #258 (Sept 1959) shows Superman dramatically exiling Supergirl from Earth. Supergirl meets Krypto for the first time, so she harmlessly plays with him – but woops, this is still early in her career when Superman has told her to keep her existence a secret – and that includes Krypto. When Superman finds out she disobeyed him, he exiles her to an asteroid for a year. Superman is being a dick!
After a week of tearful exile, she receives a note from Superman saying a cloud of kryptonite dust is passing over and she can return to the Midvale orphanage for one day. Making herself up as if she had been lost in the woods, Linda Lee returns and answers reporters questions. But one reporter, Clark Kent, drills her further. She reveals herself as Supergirl to him and Clark/Superman is crushed that Supergirl failed his “test”. However it turns out that Supergirl had already figured out that Superman was Clark Kent.
Superman then reveals that the whole incident was his final test for her to see how she handled being in a really tight spot and whether she would reveal her secret identity. He wanted to know if she could be trusted to know Superman’s other identity.
Well, now four people on Earth know who Superman really is (the others being Lori Lemaris, Batman, and Robin).