<p>We investigate the existence of Wilton ripple solutions of the Kawahara equation. Without loss of generality, these are <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(2\pi \)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mn>2</mn> <mi>π</mi> </mrow> </math></EquationSource> </InlineEquation>-periodic, traveling-wave solutions whose profiles at zero amplitude have a codimension-1 bifurcation from a linear combination of <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(\cos (x)\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mo>cos</mo> <mo stretchy="false">(</mo> <mi>x</mi> <mo stretchy="false">)</mo> </mrow> </math></EquationSource> </InlineEquation> and <InlineEquation ID="IEq3"> <EquationSource Format="TEX">\(\cos (Kx)\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mo>cos</mo> <mo stretchy="false">(</mo> <mi>K</mi> <mi>x</mi> <mo stretchy="false">)</mo> </mrow> </math></EquationSource> </InlineEquation> for <InlineEquation ID="IEq4"> <EquationSource Format="TEX">\(K \in \mathbb {N} \setminus \{1\}\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>K</mi> <mo>∈</mo> <mi mathvariant="double-struck">N</mi> <mo lspace="0.15em" rspace="0.15em" stretchy="false">\</mo> <mo stretchy="false">{</mo> <mn>1</mn> <mo stretchy="false">}</mo> </mrow> </math></EquationSource> </InlineEquation>. Using a Lyapunov-Schmidt reduction, we prove the existence of these solutions for all <i>K</i>, in contrast to previous work demonstrating existence only for <InlineEquation ID="IEq5"> <EquationSource Format="TEX">\(K = 2\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>K</mi> <mo>=</mo> <mn>2</mn> </mrow> </math></EquationSource> </InlineEquation>. Although the proof holds only for the Kawahara equation, many ideas introduced in the proof can be applied to more general contexts, including Wilton ripples of the gravity-capillary water wave equations.</p>