"When he (صلى الله علیه وسلم) got up for the second rak'ah, he would commence with All Praise be to Allaah (Faatihah 1:1), without pausing." 
He would perform this rak'ah exactly as he performed the first, except that he would make it shorter than the first, as before.
The Obligation Of Reciting Soorah Al-Faatihah In Every Rak'ah
He ordered "the one who prayed badly" to recite al-Faatihah in every rak'ah, when he said to him after ordering him to recite it in the first rak'ah , then do that throughout your prayer  (in one narration: in every rak'ah). 
He also used to say,
"There is recitation in every rak'ah." 
 Muslim & Abu `Awaanah. The pause negated in this hadeeth could be a pause for reciting an opening supplication, and not include a pause for reciting the isti`aadhah, or it could be wider in meaning than that; I find the former possibility more convincing. There are two views among the scholars regarding the isti`aadhah, and we regard the correct one as being that it is to be said in every rak`ah; the details of all this are given in al-Asl.
 Abu Daawood & Ahmad with a strong sanad.
 Bukhaari & Muslim.
 Ahmad with a good isnaad.
 Ibn Maajah, Ibn Hibbaan in his Saheeh & Ahmad in Ibn Haani's Masaa'il (1/52). Jaabir bin `Abdullaah (رضي الله عنه) said,
"He who prays a rak`ah in which he does not recite the Mother of the Qur'aan has not prayed, except behind an imaam" - related by Maalik in Muwatta'.