Adapted from a novel by Stuart Palmer, a school-teacher helps a police inspector solve a complicated murder.
Aquarium director Bertrand Hemingway (Clarence Wilson) complains on the phone that his stock broker Gerald Parker (Guy Usher) robbed him. Gwen Parker (Mae Clark) needs money and calls Philip Seymour (Donald Cook) for help. Her jealous husband Gerald slaps her. At the aquarium Gwen tells Philip that she wants to divorce Gerald. When Gerald shows up and complains, Philip knocks him out and drags away the body. A thief takes a purse and is tripped by Hildegarde Withers (Edna May Oliver); but the deaf thief Chicago Lew (Joe Hermano) escapes. Hildegarde has her school-children search for her hat-pin until it is found. Then Hildegarde finds Gerald's body in the penguin tank. Gwen sees it and faints.
Inspector Oscar Piper (James Gleason) questions witnesses, and policeman Donovan (Edgar Kennedy) catches the thief Lew. Piper accuses Philip of murder and also tells Gwen she could have killed Gerald. Philip confesses that he drowned him; but Hildegarde says that is false. Piper learns that Gerald was not drowned. Piper questions Gwen's lawyer Barry Costello (Robert Armstrong). Hildegarde tells Piper of stains on Gwen's stockings. Hemingway denies that he quarreled with Gerald, but Hildegarde shows a letter proving he did. A hat found in the tank was not the victim's. Donovan is found after being hit on the head.
Hildegarde feeds Piper and gives him typed notes. Piper learns that Gerald was killed in the ear and suspects that Hildegarde's hat-pin was used. Hildegarde goes to Gerald's office, satirizing the receptionist's use of make-up. Piper tells Hildegarde that Gwen will testify against Philip. The stain proves that Gwen was near the tank. In jail Philip tells them he thinks Gwen did it, and Gwen is arrested. Hildegarde and Costello go to the aquarium at night and find the hat-band removed from a penguin's throat by Hemingway. Hildegarde calls Piper and screams as the lights go out. The hat-band is found in Hemingway's pipe. Piper has Hemingway arrested too. Costello tells Piper that Lew knows who did it; but Lew is found hanged in jail by wire. Costello admits he smuggled the wire to Philip and explains how Philip could have killed Lew. In a trial Costello defends Gwen and asks Hildegarde if she had an affair with Gerald. Hildegarde says that Costello is the murderer, because he knows Gerald was stabbed in the right ear. Gwen says that Costello was her lover. Costello pulls a gun, but Piper grabs him. Piper and Hildegarde discuss how Costello tried to plant evidence. Piper proposes, and Hildegarde accepts.
This detective tale is highlighted by the amusing cleverness of the feminist Hildegarde, who is a better detective than the inspector.