Term to a verse that starts with the last word of the previous verse

The music "Glad you came" by The Wanted has the following verses

Turn the lights out now, now I'll take you by the hand

Hand you another drink, drink it if you can

Can you spend a little time, time is slipping away

Away from us so stay, stay with me I can make

Make you glad you came

Is there a term for it?


Solution 1:

Anadiplosis: repetition of the final words of a sentence or line at the beginning of the next

Examples

Solution 2:

It's a form of chain verse, or a chain rhyme: http://en.wikipedia.org/wiki/Chain_rhyme