Police were called to an address in Laing Road at around 5.35am on Sunday 17 January.
Once there, officers discovered that a woman was unresponsive inside the property.
The victim, a woman in her 20s, was later pronounced dead at the scene despite the best efforts of paramedics.
A 21-year-old local man has been arrested on suspicion of murder.
Police believe that the parties involved were known to each other.
At this time they are not looking for anyone else.
If you have any information about this incident please call our Major Crime Team on 101 and quote incident number 193 of 17 January.