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This paper addresses the computational problem of deciding invertibility (orone to one-ness) of a Boolean map $F$ in $n$-Boolean variables. This problemhas a special case of deciding invertibilty of a map$F:\mathbb{F}_{2}^n\rightarrow\mathbb{F}_{2}^n$ over the binary field$\mathbb{F}_2$. Further the problem can be extended and stated over a finitefield $\mathbb{F}$ instead of $\mathbb{F}_2$. Algebraic condition forinvertibility of $F$ in this special case over a finite field is well known tobe equivalent to invertibility of the Koopman operator of $F$ as shown in\cite{RamSule}. In this paper a condition for invertibility is derived in thespecial case of Boolean maps $F:B_0^n\rightarrow B_0^n$ where $B_0$ is the twoelement Boolean algebra in terms of \emph{implicants} of Boolean equations.This condition is then extended to the case of general maps in $n$ variables.Hence this condition answers the special case of invertibility of the map $F$defined over the binary field $\mathbb{F}_2$ alternatively, in terms ofimplicants instead of the Koopman operator. The problem of decidinginvertibility of a map $F$ (or that of finding its $GOE$) over finite fieldsappears to be distinct from the satisfiability problem (SAT) or the problem ofdeciding consistency of polynomial equations over finite fields. Hence the wellknown algorithms for deciding SAT or of solvability using Grobner basis forchecking membership in an ideal generated by polynomials is not known to answerthe question of invertibility of a map. Similarly it appears that algorithmsfor satisfiability or polynomial solvability are not useful for computation of$GOE(F)$ even for maps over the binary field $\mathbb{F}_2$.

Deciding One to One property of Boolean maps: Condition and algorithm in terms of implicants