an electrically conductive alumina fiber which heretofore known only as electrically insulative is now provided , which comprises an aluminum oxide matrix , and a continuous phase of carbon in the aluminum oxide matrix , the continuous phase of carbon affording an electrically conductive property to the fiber . also , a method of producing the alumina fiber is disclosed , comprising pyrolyzing a fiber of polyaloxane ] having a formula ## str1 ## wherein , r 1 represents ch 2 ch 2 och 2 ch 3 , r 2 represents ## str2 ## or other substituted aromatic group , in an inert atmosphere .