<p>Correctors, also known as post-processing functions, are used to reduce or eliminate statistical weaknesses of the raw sequences generated by True Random Number Generators (TRNGs). The correction order and nonlinearity are two important criteria of the correctors, and higher values for both are desirable. In a recent work by Zhang (IEEE Trans Inf Theory 69(10): 6671–6681, 2023), constructions of correctors with high nonlinearity and correction order have been presented. In this paper, we investigate the constructions of correctors in detail. First, we introduce the concept of <i>n</i>-variable resilient fragmentary functions, a special class of functions defined on subsets of <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(\mathbb {F}_2^n\)</EquationSource> <EquationSource Format="MATHML"><math> <msubsup> <mi mathvariant="double-struck">F</mi> <mn>2</mn> <mi>n</mi> </msubsup> </math></EquationSource> </InlineEquation>. By using these functions, we construct semi-bent correctors with the highest known correction order, thereby achieving a good trade-off between nonlinearity and correction order. Furthermore, we combine the Generalized Maiorana-McFarland (GMM) technique proposed by Zhang and resilient fragmentary functions to construct correctors that have the best known nonlinearity compared to those of known resilient Boolean functions. Additionally, their algebraic degree can be optimized through slight modifications. All the correctors we constructed in this paper possess a correction order that exceeds their resiliency order.</p>