This paper deals with a generalization of the following simple observation. Suppose there are distinct elements a, b of the chain complete poset (P, <) such that P( < a) C P( < b) and P( > a) L P( > h); if P( < a) and P( > a) are both fixed point free (fpf), then P is also fpf (we say P is trivially fpf), otherwise, P has the fixed point property (fpp) if and only if P(u) has this property. We introduce a new quasi-order on a poset (P, < ), called the ANTI-order denoted by <<, where x<<y holds if and only if every element strictly comparable with x is also strictly comparable with y. A set X C P is an ANTI-good subset of P, if X is maximal (with respect to inclusion) and its elements are <<-maximal and pairwise <<-incomparable. A poset (P, <) is caccc if it is chain complete and every countably infinite antichain has a supremum (infimum) whenever the antichain is bounded above (below). The caccc property is preserved by retracts and the intersection of a decreasing chain of caccc subposets also has this property. We show that for a caccc poset (P, Q ) an ANTI-good subset is a retract and it is uniquely determined up to isomorphism. Moreover, if P is not trivially fpf, then P has the fpp if and only if an ANTI-good subset has the fpp. A strictly decreasing sequence, I7 = (Pi;: 5 < A), of subsets of a caccc poset P is called an ANTI-perfect sequence of P, if P = Pa and, for each [ < i,, PC+, is a <<r-good subset of PC, where <<: is the ANTI-order on P;, and P; = n{P,: q < [} when 5 is a limit ordinal, and Pj: is a <<;-good subset of itself. We call Pi an ANTI-core of P. Our main result is that an ANTI-core of a caccc poset is a retract. The proof of this will be given separately in the second part of the paper [5]. In this part we establish the existence of ANTI-perfect sequences.