Goal recognition is an important problem in many application domains (e.g., pervasive computing, intrusion detection, computer games, etc.). In many application scenarios, it is important that goal recognition algorithms can recognize goals of an observed agent as fast as possible. However, many early approaches in the area of Plan Recognition As Planning, require quite large amounts of computation time to calculate a solution. Mainly to address this issue, recently, Pereira et al. developed an approach that is based on planning landmarks and is much more computationally efficient than previous approaches. However, the approach, as proposed by Pereira et al., also uses trivial landmarks (i.e., facts that are part of the initial state and goal description are landmarks by definition). In this paper, we show that it does not provide any benefit to use landmarks that are part of the initial state in a planning landmark based goal recognition approach. The empirical results show that omitting initial state landmarks for goal recognition improves goal recognition performance.