If you do it right, sure. It's called a clone. Search around here for threads about taking clone clippings. You need to do it in the right spot, and generally you need some sort or rooting solution to promote formation of a new root system.
yup, take the part above the leaf, use clean sharp tool to cut this off. Then I split the stem of what I cut off vertically for about an 1/2 in. I dip it in [ame="http://www.amazon.com/dp/B004NEBR1U/ref=asc_df_B004NEBR1U1632482?smid=ATVPDKIKX0DER&tag=shopzilla_rev_267-20&linkCode=asn&creative=395093&creativeASIN=B004NEBR1U"]Shultz brand[/ame] rooting hormone and place it right in a peat pellet keep it moist and the entire cutting humid. In 2 to 3 weeks it will start to root then slap the girl in some dirt. You can use what ever rooting hormone you want and you don't have to cut the stalk vert. either that is just how I do it.