Yes, the day after Hitler's death, on 31 April 1945, Goebbels was made Führer. The same day, he had an SS-Stabsveterinär administer morphine to his six children (Goebbels also had a stepson but he was captured by the Western Allies in Italy in 1943) before administering cyanide. Magda Goebbels just proceeded to play with cards and smoke immediately after as if nothing had happened. They both committed suicide that day, with accounts as to how they did so varying.