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In this work, we consider the properties of the two-term Machin-like formula and develop an algorithm for computing digits of <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>π</mi></semantics></math></inline-formula> by using its rational approximation. In this approximation, both terms are constructed by using a representation of <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mn>1</mn><mo>/</mo><mi>π</mi></mrow></semantics></math></inline-formula> in the binary form. This approach provides the squared convergence in computing digits of <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>π</mi></semantics></math></inline-formula> without any trigonometric functions and surd numbers. The Mathematica codes showing some examples are presented.