The article deals with the criticism of the nationalist-cum-religious nature of the State of Israel, developed by the Israeli New Left organisation commonly known by the name of its press organ 'Matzpen' (Hebr. compass). The development of Matzpen's anti-Zionist concepts is shown from the birth of that organisation to Yom Kippur war (of 1973). The views of Matzpen are juxtaposed to the classic anti-Zionist document of Marxist Left that was independent of the Kremlin, namely, the resolution 'Israel vs. the Arab Revolution', passed by the U.S. Socialist Workers' Party (SWP) in 1971. The position of Matzpen, which acknowledged Israel's right to existence, was to become a minority view among the New Left organizations, compared to the denial of such right, represented, for example, by the aforementioned SWP. Despite its small size, Matzpen and its activists staying in the West were profoundly significant for the New Left, providing it with evidence that radical anti-Zionism free of any suspicions of anti-Semitic inspiration was possible.