"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." [1]
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 [2], then do that throughout your prayer [3] (in one narration: in every rak'ah). [4]
He also used to say,
"There is recitation in every rak'ah." [5]
Footnotes
[1] 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.
[2] Abu Daawood & Ahmad with a strong sanad.
[3] Bukhaari & Muslim.
[4] Ahmad with a good isnaad.
[5] 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'.