All perfect praise be to Allah the Lord of the Worlds. May His peace and blessings be upon our Prophet Mohammad and upon all his family and companions.
It is recommendable to recite Basmalah before reciting any Soorah, be it new or repeated since Basmalah is a verse from every Soorah (Chapter of Quran) except the Soorah entitled "Bara`ah." The evidence on this is that Anas reported: One day the Messenger of Allah (Blessings and peace be upon him) was sitting amongst us that he dozed off. He then raised his head smilingly. We said: What makes you smile. Messenger of Allah? He said: A Sura has just been revealed to me, and then recited: In the name of Allah, the Compassionate, the Merciful. Verily We have given thee Kauthar (fount of abundance). Therefore turn to thy Lord for prayer and offer sacrifice, and surely thy enemy is cut off (from the good)." {Related by Muslim, No.400}.
This is the reliable view in our Madhab (Shafie), so it is recommendable for a person to recite Basmalah so as not to miss any part of the Soorah and this ruling applies when repeating the same Soorah or reciting different Soorahs during Ruqyia Shariya* or other Awrad.*
An-Nawawi (May Allah be pleased with him) said: "It is recommendable for a person to recite "Bismillah Ar-rahman Ar-Raheem" before reciting any Soorah except "Bara`ah" because most scholars stated that it is considered a verse wherever it is written in the Quran and it is written at the beginning of every Soorah except "Bara`ah".
Consequently, if a person recites Basmala, then, there is no dispute amongst scholars that he/she has recited the whole Quran. But, if he/she doesn`t recite it, then he/she has left some of the Quran, as stated some scholars." {At-Tibyaan, pp.37}.
Moreover, Ibn Hajar said: "The more correct opinion is that Basmalah is a complete verse from every Soorah except "Bara`ah." {Tohfat Al-Mohtaaj, vol.2/pp.36}. And Allah The Almighty Knows Best.
*Ruqyah refers to the healing method based on the Quran and hadith through the recitation of the Quran, seeking of refuge, remembrance and supplication that is used as a means of treating sickness and other problems, by reading verses of the Quran, the names and Attributes of Allah, or by using the prayers in Arabic or in a language the meaning of which is understood.
*The wird (plural: awrād) is a regular litany and a mystical invocation practiced by murids and saliks and wassils in islamic sufism.