A new and distinct cultivar of Red Bayberry, botanically known as Myrica rubra, and hereinafter referred to by the name ‘N1MR06’ is described. ‘N1MR06’ produces fruit having improved sweetness, a good sugar:acid ratio, a palatable low resin taste along with uniform fruit size and colour. N1MR06 has the following traits: mean fruit diameter is 21.4 mm mean fruit weight is 5.87 g fruit colour is red-black mean fruit flesh total soluble solids (an indicator of sweetness) is 12.0° Brix mean fruit flesh titratable acidity is 1.41% and fruit harvest season in the southern hemisphere is early-mid November.