On his return from Italy, Klein would soon have reinstated his strict regime of piano practice. He also composed. He made some short sketches, dated 22 September, for a chamber work for piano and brass, possibly inspired by Janáček's Capriccio for piano and small ensemble, a work with which he was familiar. That same month, he completed his most ambitious work to date, the Four Movements for String Quartet, dedicated to Lisa, a piece he had been working on since the summer of 1936. Indeed, her brother acknowledges the slow gestation of the Four Movements when, at the end of the manuscript, he writes, ‘Completed after two years of work on the first of June 1938’, even though the revised fair copy was not signed off until the September date. The sketch for the second movement originally included a part for voice. Though this idea was dropped after a few bars, it shows that he was still interested in this combination, recalling his earlier sketches of a quartet with solo voice.

Considering that its composer was only sixteen when he began this piece, it is remarkable in a number of ways. First, its four movements last barely fifteen minutes, and yet are concentrated in concept, exploring his characteristic compositional pre-occupation with intricate, modernistic polyphony. Second, his acknowledgement of a contrapuntal style is stated outright, as the first four notes in the solo viola spell out BACH, a formula employed by Bach himself and many others, and in other drafts of incomplete works by Klein himself. These notes, normally adjacent, are displaced, so that he achieves his now distinctive angularity of melodic shape. It is unknown whether he felt that his compositional style lacked the profound logic one usually associates with the title of ‘string quartet’, or that the genre was too encumbered with historical baggage. Certainly, he does not adhere to the closed forms of the Classical string quartet, and yet by the 1930s the string quartet had evolved into one which was no longer hampered by convention. In the event, Klein's work does demonstrate stylistic cohesion, in music which is influenced by both the Second Viennese School and Janáček.