There is another theory that it was a custom of the Ashikaga clan in the Muromachi period to eat red and white lozenge-shaped rice cakes during the New Year's holidays, and when these were introduced to the imperial court, a layer of kusa mochi was added, giving rise to hishi mochi.
室町時代の足利氏には正月に紅白の菱形の餅を食べる習慣があり、宮中に取り入れられて草餅と重ねて菱餅になったという説がある。