One type of two-dimensional diamonds that are derived from [111] direction, so-called diamane, has been previously shown to be stabilized by N-substitution, where the passivation of dangling bonds is no longer needed. In the present work, we theoretically demonstrated that another type of two-dimensional diamonds derived from [110] direction exhibiting a washboard conformation can also be stabilized by N-substitution. Three structural models of washboard-like carbon nitrides with compositions of C6N2, C5N3, and C4N4 are studied together with the fully hydrogenated washboard-like diamane (C8H4). The result shows that the band gap of this type structure is only open the dangling bonds that are entirely diminished through N-substitution. By increasing the N content, the C11 and C22 are softer and the C33 is stiffer where their bulk modulus are in the same order, which is approximately 550 GPa. When comparing with the hydrogenated phase, the N-substituted phases have higher elastic constants and bulk modulus, suggesting that they are possibly harder than the fully hydrogenated diamane.