C. muelleri is a
clustering, climbing palm growing up to in length, with thin stems up to diameter. The
pinnate fronds are
alternate and more or less
sessile. They are up to long with 7-13 leaflets on each side and have long recurved spines on the
rachis. The leaflets have spines along the midrib on the upper surface and small sharp spurs on their margins. The leaf sheath is densely covered in spines. This species, like others in the genus, produces a modified sterile
inflorescence (known as a flagellum) up to long, which is armed with dozens of strong, recurved barbs that act like
grappling hooks to latch on to nearby vegetation and provide support for the plant. Fertile inflorescences are up to long and flowering occurs in all months of the year. The fruits are a
globose drupe about in diameter, containing a single seed. ==Taxonomy==