  We present necessary and sufficient conditions for a Boolean function to be a
negabent function for both even and odd number of variables, which demonstrate
the relationship between negabent functions and bent functions. By using these
necessary and sufficient conditions for Boolean functions to be negabent, we
obtain that the nega spectrum of a negabent function has at most 4 values. We
determine the nega spectrum distribution of negabent functions. Further, we
provide a method to construct bent-negabent functions in $n$ variables ($n$
even) of algebraic degree ranging from 2 to $\frac{n}{2}$, which implies that
the maximum algebraic degree of an $n$-variable bent-negabent function is equal
to $\frac{n}{2}$. Thus, we answer two open problems proposed by Parker and Pott
and by St\v{a}nic\v{a} \textit{et al.} respectively.
