I need to write text from a recorded speech archive. Is it possible to write it directly without listening to the voice which is already record it?
I agree that you would still have to listen to the recording and review anything that you have nit personally transcribed due to technical, spelling, and other errors. Honestly, proofing and editing previously transcribed work, especially when you are not the one that did the work, trends to become more time consuming and tedious than necessary. As Oron stated, any software needs to be "trained" by specific voices and how words are spoken, and any other human would need to know the context of the audio, such as knowing medical terminology and medicine for medical transcriptions.
It would be nice if transcription was as easy as letting software scan audio files and giving a written document of everything that was said (and by whom, if applicable). This, unfortunately, will not happen any time soon, especially since not everything spoken is clean, clear, or even the correct pronunciation.
While there are voice recognition software packages out there, none of them are really up to the job of unattended transcription. The better ones (Nuance Dragon Dictate etc) require training for a particular voice and will not be accurate with other people's voices. In some specific domains (e.g. phone menu systems, Siri etc) it is possible to get good accuracy even without voice & accent training, but that is mostly because the vocabulary is limited. The technology simply isn't up to the job yet, and my feeling is it's going to be some time before it is.
Try VoiceBase; it's a web service (not good if your audio needs to be confidential), but it'll do the job.
There's a link to Freemake Free Audio Converter in the linked article if the audio file(s) are not in a format compatible with the service.
Of course you could try a speech recognition software but that doesn't eliminate the necessity to listen over the audio and check whether everything was done correctly.
Depending on the age and quality of the audio archive you might be better off doing the actual transcription yourself in the first place.