Last year police in Scotland recorded 62 cases, down from 93 in the previous year, according to official figures.
More than three-quarters of homicide cases took place in a residential location, the statistics show.
About half of all victims were killed by someone they knew, and 43% of the accused were under the influence of drink or drugs.
Justice Secretary Kenny MacAskill said: "We are making progress and this trend is to be welcomed, but we can't forget that behind these figures are the grieving families of 62 victims having to cope with the death of a loved one.
"It remains the case, as in previous years, that victims are mostly male, killed by someone they know, in a house or flat with the accused often under the influence of alcohol or drugs. The figures confirm that we are right to continue to take action to encourage people away from excessive alcohol consumption. Recreational drug use is also falling, particularly among young people."
The most common method of killing over the past decade was with a sharp instrument such as a knife.
In 2012-13, 26 people were killed this way, accounting for 42% of recorded victims.
Assistant chief constable Malcolm Graham, the lead officer for major crime and public protection for Police Scotland, said: "We recognise the significant impact that any homicide has on a range of people, from victims themselves and their families to the wider community, so it is also welcome that we have seen the lowest number of victims in 37 years."
John Carnochan, co-founder of the Violence Reduction Unit, said: "This is really positive but there is a danger in looking at statistics that we will think this problem is fixed but in reality we need to understand it better and understand how and why it is shifting."
"If, as it seems, violence is moving indoors, we need to do more about that."
Police identified one or more accused people in 61 of the 62 cases.