Greedy codes are obtained by arranging the binary vectors of length \(n\) in some ordering, selecting the first vector for the code and then, preceeding once through the ordering, selecting a vector if it differs in at least \(d\) positions from all previously selected vectors. It is well-known that greedy codes are linear if the ordering satisfies some properties. The author shows that the linearity remains valid if we stipulate that all code vectores are orthogonal to themselves and the other code vectors. Examples include self-orthogonal \([8,4, 4]\), [22,11,6] and [24,12,8] codes. It is shown that under certain conditions, the greedy self-orthogonal code is not a subcode of the greedy code of equal length and minimum distance.