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The non-Gaussian nature of the epoch of reionization (EoR) 21-cm signal has asignificant impact on the error variance of its power spectrum $P({\bf\textit{k}})$. We have used a large ensemble of semi-numerical simulations andan analytical model to estimate the effect of this non-Gaussianity on theentire error-covariance matrix ${\mathcal{C}}_{ij}$. Our analytical model showsthat ${\mathcal{C}}_{ij}$ has contributions from two sources. One is the usualvariance for a Gaussian random field which scales inversely of the number ofmodes that goes into the estimation of $P({\bf \textit{k}})$. The other is thetrispectrum of the signal. Using the simulated 21-cm signal ensemble, anensemble of the randomized signal and ensembles of Gaussian random ensembles wehave quantified the effect of the trispectrum on the error variance${\mathcal{C}}_{ij}$. We find that its relative contribution is comparable toor larger than that of the Gaussian term for the $k$ range $0.3 \leq k \leq 1.0\,{\rm Mpc}^{-1}$, and can be even $\sim 200$ times larger at $k \sim 5\, {\rmMpc}^{-1}$. We also establish that the off-diagonal terms of${\mathcal{C}}_{ij}$ have statistically significant non-zero values which arisepurely from the trispectrum. This further signifies that the error in different$k$ modes are not independent. We find a strong correlation between the errorsat large $k$ values ($\ge 0.5 \,{\rm Mpc}^{-1}$), and a weak correlationbetween the smallest and largest $k$ values. There is also a smallanti-correlation between the errors in the smallest and intermediate $k$values. These results are relevant for the $k$ range that will be probed by thecurrent and upcoming EoR 21-cm experiments.

Statistics of the epoch of reionization 21-cm signal - I. Power spectrum error-covariance