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A great part of missing daily relative sunspot numbers in the time interval 1749–1848 was reconstructed by nonlinear two-step method of interpolation. In the first step gaps of missing observations not longer than five days were directly interpolated. In the second step data were sorted to so-called Bartels scheme, i.e., to rows of the length of 27 days subsequently ranged in a matrix. In this step the missing value at any position was interpolated from the data at the same position of preceding and following rows. The interpolation was limited to sequences of no more than four missing data. The procedure enables to interpolate long gaps and simultaneously to respect the 27-day variation of solar activity. Monthly and annual means of relative sunspot numbers are presented. The differences between monthly and annual means of the primary observations and of the data completed by interpolation fluctuate around zero. The amplitude of fluctuations depends inversely on the frequency of observations. Most conspicuous are the deviations in the time interval 1776–1795 where the frequency of observations is very low or almost zero. The average dispersion σ of monthly differences is ±11.5 R and that of annual differences is ±7.8 R. The two-step method of interpolation was tested on the series of daily data in the time interval 1918–1948. The sequence of missing daily data in the years 1818–1848 represents a masking function. This function was applied to the continuous data series in the time interval 1918–1948 and then the modified series was reconstructed. The differences between the monthly and annual means of primary and reconstructed data are small with fluctuations around zero and with dispersion σ for monthly differences ±2.7 R a for annual differences ±0.6 R. Corresponding dispersions σ of the data differences for monthly means in the time interval 1818–1848 are ±4.3 R and ±1.1 R for annual means. The small dispersion values and small differences among them give evidence about the applicability and the effectiveness of the nonlinear two-step method of interpolation and also about high credibility of relative sunspot numbers after reconstruction.