diff --git a/k2/csrc/intersect_dense_pruned.cu b/k2/csrc/intersect_dense_pruned.cu
index e612921ac..8a0fe400d 100644
--- a/k2/csrc/intersect_dense_pruned.cu
+++ b/k2/csrc/intersect_dense_pruned.cu
@@ -381,6 +381,11 @@ class MultiGraphDenseIntersectPruned {
         ArcInfo old_ai = arcs_data[old_idx012];
         // Only 1 state (the final state) in next frame, so idx1 is always 0.
         old_ai.u.dest_info_state_idx1 = 0;
+        // The final arcs we are adding for online decoding partial should not
+        // map to any real arc in a_fsas.
+        // We add these final arcs for the purpose of making the partial lattice
+        // a valid Fsa.
+        old_ai.a_fsas_arc_idx012 = -1;
         new_arcs_data[new_idx012] = old_ai;
     });