Remove the seat by undoing the bolts that attach it to the frame on each side. Place the washers and nuts somewhere for safe keeping.
Cut away the cane and remove the spline. Leave about 2 inches of cane around the seat's frame. It will come up with the spline once treated with some drops of hot water water. Drizzle warm water over the spline to make it pliable and loosen the glue holding it and the remaining cane in place. It may take some time to loosen, but will come eventually.
Scrape the seat to rid it of any excess glue and bits of cane. Allow it to dry overnight to ensure that the new spline and cane will take hold when you replace it.
Soak the cane webbing and the new spline in warm water for about 15 minutes, until it is pliable. Shake off any excess water.
Position the cane over the seat so the shiny side is up. Tap the cane in place with a wedge. Start at the back and allow for some give in the middle of the seat because the cane will shrink as it dries. Add some wood glue to the cane and tap the spline in place.
Cover the seat with a damp towel to regulate the drying process. Move it outside and allow it to dry for 24 hours.
Cut any excess cane from the dry seat and reassemble your bentwood rocker.