This work contributes to investigate theoretical properties of the trend vanishing moment (TVM) which the authors have defined in a previous work and applied to the directional design of 2-D nonsep-arable GenLOTs. The TVM condition can be regarded as a natural extention of 1-D VM to 2-D one and alternative of the conventional directional vanishing moment (DVM). Firstly, the definition of TVM is given to clarify what it is, and then the mathematical meaning is discussed. While the conventional DVM condition requires for the moments to vanish along lines in the frequency domain and restricts the direction to a rational factor, the TVM condition imposes the moments only point-wisely and the direction can be steered flexibly. Some significant properties of TVMs are also shown and a simulation result of zonal coding for an artifical picture is given to verify the trend surface annihilation property. © 2010 IEEE.