V članku je podan nov in bolj učinkovit dokaz našega prejšnjega rezultata, da ima vsaka ▫$2 \times 2$▫ Toeplitzova matrika ▫$M$▫ reprezentirajočo mero, ki je optimalna v smislu, da je ▫$\Vert \mu ...\Vert = \Vert M \Vert_S$▫, kjer je na desni strani norma matrike ▫$M$▫ kot Schurovega multiplikatorja. Pokažemo, da ta rezultat sledi iz elementarnih ugotovitev o ekstremnih točkah enotske krogle v prostoru trigonometričnih trinomov. V nadaljevanju podamo popolno karkaterizacijo takih ekstremnih točk.
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