I don't think it is usual practise to prune them ,Fay..as they grow from the top.Only take off any old dead and brown leaves around the bottom of the trunk.which should pull away easily,or if not,cut them off closely..Are you in a frost zone ? If so,they may need protecting in a really cold spell..A lot were lost here this last winter...but some did regrow from the base in late spring,and then when it was certain that it was dead, the dead foliage and trunk was cut off.Some grew more than one stem,to make a bushier plant ..

thank you for your help . making friend throuhg gardening is so wonderful. fay fahout

Welcome to GoY,Fay..everyone is very helpful and friendly on here ..

I used last winter's dead trunks to grow a clematis up, and sure enough the cordyline has since sprouted again at its base!

If it is an outside plant that you want to branch, or develop offsets, try feeding it a bit, especially if it is in a pot. Indoors, feeding should be accompanied with more light--and possibly a larger pot, if less than 1/5 as wide as the plant is tall.

Mostly they don't get pruned - but you often end up with a very tall trunk with a plume of foliage right at the top. If you don't want that, it's fine to saw the thing down, either to the ground, or halfway down, to force new growth. Trouble is, some of that new growth is bound to be at the base, so its up to you. Best done in late spring.

Some parts of Australia can grow seven or eight different species of Cordyline, too. Do you know which one this is, Fay? Or, can you post a picture?