<p>Turyn-type sequences, <i>TT</i>(<i>n</i>), are quadruples of <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="12095_2025_829_Article_IEq1.gif" Format="GIF" Height="19" Rendition="HTML" Resolution="72" Type="Linedraw" Width="44" /> </InlineMediaObject> <EquationSource Format="TEX">\({\{\pm 1\}}\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mo stretchy="false">{</mo> <mo>±</mo> <mn>1</mn> <mo stretchy="false">}</mo> </mrow> </math></EquationSource> </InlineEquation>-sequences <i>X</i>,&#xa0;<i>Y</i>,&#xa0;<i>Z</i>,&#xa0;<i>W</i> with lengths <InlineEquation ID="IEq2"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="12095_2025_829_Article_IEq2.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="94" /> </InlineMediaObject> <EquationSource Format="TEX">\({n, n, n, n-1}\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>n</mi> <mo>,</mo> <mi>n</mi> <mo>,</mo> <mi>n</mi> <mo>,</mo> <mi>n</mi> <mo>-</mo> <mn>1</mn> </mrow> </math></EquationSource> </InlineEquation> respectively, such that a certain sum of their respective nonperiodic autocorrelation functions is always equal to 0. Turyn-type sequences are known to exist for all even <InlineEquation ID="IEq3"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="12095_2025_829_Article_IEq3.gif" Format="GIF" Height="15" Rendition="HTML" Resolution="72" Type="Linedraw" Width="51" /> </InlineMediaObject> <EquationSource Format="TEX">\({n \le 38}\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>n</mi> <mo>≤</mo> <mn>38</mn> </mrow> </math></EquationSource> </InlineEquation>. In this paper we construct the first examples of <i>TT</i>(40), <i>TT</i>(42), <i>TT</i>(44). Each one of these new Turyn-type sequences gives rise to an infinite series of Hadamard matrices among various other consequences.</p>