<p>In this paper, we introduce a new method for obtaining the united inner solution set of the interval Lyapunov matrix equation <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(AX+XA^T\approx {\textbf {B}}\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>A</mi> <mi>X</mi> <mo>+</mo> <mi>X</mi> <msup> <mi>A</mi> <mi>T</mi> </msup> <mo>≈</mo> <mi mathvariant="bold">B</mi> </mrow> </math></EquationSource> </InlineEquation>, where <i>A</i> is a given square real matrix, <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\({\textbf {B}}\)</EquationSource> <EquationSource Format="MATHML"><math> <mi mathvariant="bold">B</mi> </math></EquationSource> </InlineEquation> is a given interval matrix, and <InlineEquation ID="IEq3"> <EquationSource Format="TEX">\({\textbf {X}}\)</EquationSource> <EquationSource Format="MATHML"><math> <mi mathvariant="bold">X</mi> </math></EquationSource> </InlineEquation> is an unknown interval matrix. The approach is based on the use of <InlineEquation ID="IEq4"> <EquationSource Format="TEX">\(\{1\}\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mo stretchy="false">{</mo> <mn>1</mn> <mo stretchy="false">}</mo> </mrow> </math></EquationSource> </InlineEquation>-inverses of the coefficient matrices of the associated interval linear system, which makes it applicable to singular systems. We derive a necessary and sufficient condition for the consistency of the equation and present an algorithm for computing an inner interval estimate of its united solution set. We demonstrate the use of the obtained results through illustrative examples.</p>