Yes, but it's also okay to use "Yours sincerely" in formal letters. The difference is that we use "Yours faithfully" when we start a letter with "Dear Sir/Madam", while "Yours sincerely (or Sincerely yours)" is used when we've mentioned the actual name of the person you're writing to in the salutation.
Formal, we don't know the name of the person:
Formal, addressed to a particular person:
Dear Ms Paula Hill,
"Yours sincerely" is typically employed in English when the recipient is addressed by name (e.g. "Dear John") and is known to the sender to some degree.
"Yours faithfully" is used when the recipient is not addressed by name (i.e. the recipient is addressed by a phrase such as "Dear Sir/Madam") or when the recipient is not known personally by the sender.
In American English, "Sincerely yours" or "Sincerely" are commonly used in formal correspondence. "Faithfully yours" is rare.
"Yours truly" is also used in professional correspondence when writing to a client by his name, but signing the letter in the name of the firm where neither "Yours faithfully" or "Yours sincerely" would be appropriate
Dear Mr. Brown,
Commonly appearing in the US as "Yours truly," or "Yours very truly," use in the UK was an indication that the recipient was of a higher status than the signatory.
For those who pay attention to old-fashioned manners, "Sincerely yours" is regarded as appropriate only for social correspondence, and not business correspondence.
Closings such as "Cordially" or "Best regards" are always inappropriate for business letters to strangers, and their use may be considered silly and uninformed by the recipient.
I was taught a saying:
I am sincere, you are faithful.It doesn't matter who you write to in the heading either the name or Sir/Madam.
What is important is whether you are writing in the first person singular or third person. Therefore if you are writing as
we then one would use "yours faithfully" but if one uses
I then it should be "yours sincerely".