Holmboe's last quartet work, which is unofficially also String Quartet No. 21, was the last work he ever composed, and was unfinished on his death in 1996. His pupil Per Nørgård has finished the quartet, and himself characterizes his contribution by saying that the score existed “in an only partly completed form, which could however be written out with only a few cases of doubt”. With only two movements and a playing time of about nine minutes it is at its existing length the shortest of Holmboe's string quartets. The first movement takes the form of one long arch in a rocking triple time which constantly shifts among different tempo and pulse sensations. At the same time the rhythmic energy increases until the movement, in a faster Con moto tempo accelerates to a more flowing 12/8 time, coloured both rhythmically by cross-rhythms in duple time and timbrally by harmonics in the viola. In its middle section, Con fuoco, the movement culminates in both tempo and expression until it falls calm in brief recapitulations in reverse order of the first two sections. The rocking feeling continues in the second movement, but now at a more extroverted level from the outset, Allegro and pizzicato. The energy builds up further as the mood intensifies to Con fuoco, while all instruments go over to bowed playing, but like the first movement, this movement ends Adagio - here however not as a gradual attenuation but through a sudden shift in tempo to a calm, imitative passage before the movement slowly thins out to the almost inaudible through a last, dense, open-sounding chord with a brief violin solo above it.
The quartet is dedicated to Holmboe's wife MeLa May Holmboe, and was given its first performance by the Kontra Quartet on 22nd March 1997 at the Carl Nielsen Academy of Music in Odense, Denmark.