Could Time-Turner be used to save Black?

[nakedhermione]

No: HPFGUIDX 82116

A thousand pardons to the group if this question has already been 
asked but...
Could the Time-Turner used by Hermione in POA (to save Black the 
first time) also be used to go back in time and save Sirius from 
being killed by Bellatrix in OOTP? If so, why hasn't any of 
Dumbledore's crew thought of it? Is it not possible after someone has 
already died?

                                        Now, no peeking,
                                         NakedHermione