In this contribution, some modifications are proposed to the triangle prediction merge index coding. In the current design, a 40x3 size table has to be saved to map 40 group of (partition orientation, merge index 1, merge index 2) values to table index values for signaling. According to this proposal, partition orientation is signaled separately from merge indexes. Another separate flag is signaled to indicate how merge index 1 and 2 are mapped to the two triangle partitions. With the proposed method, the table size is effectively reduced to 10x2. The reported results show no performance impact with the proposed simplifications. In addition, a bug fix is reported in the contribution on triangle mode flag signaling, which results in minor coding performance gain.