We make the translations of our partitions from [3] in the context of all countable subsets of a fixed uncountable set. A different translation was obtained recently by Velleman [4]. The purpose of this paper is to define a two-cardinal version of one of our partitions from [3]. Theorem. For every uncountable set A there is a c :[[A]f0]]2 -* A such that, for every cofinal U C [AfQ' and a in A, there exist x c y in U such that c(x, y) = a. The proof will use straightforward generalization of one of the partitions from [3]. We shall assume that A is equal to some initial ordinal 0, and we shall fix an r: [0]8--+ {O, 1}w such that rx $ ry for x c y. [Identifying w1 with a subset of {O, 1}t, let rx (including finite x) be the standard code of (tp x, qx), where qx is defined recursively on sup x as follows assuming that, for each ordinal a of cofinality co, we have a fixed increasing sequence {ai} converging to a: If x has a maximal element 4 set qx(0) = 1 and qx(i + 1) = ry(i), where y = x nf . If a = sup x is a limit ordinal, let qx(O) = 0 and qx(2'(2j + 1)) = rx (j), where xi =x n ai.] Moreover, we shall fix a one-to-one ex : x -c o for each x in [0*"0 . For an integer n and x in [0]Ro, we set x(n) = 4E x: ex(4) < n}. For x c y in [Qfo0, let A(X , Y) = /\(rx, ry), i.e., the minimal place where the reals rx and ry disagree. Finally, for x c y in [6]fO and an ordinal A < 0, we set cA(x, y) = min(y(A(x, y)) \ sup(x n A)), Received by the editors October 10, 1989 and, in revised form, February 9, 1990. 1980 Mathematics Subject Classification (1985 Revision). Primary 03E05, 04A20. Research at MSRI supported in part by NSF Grant DMS-8505550. i) 1991 American Mathematical Society 0002-9939/91 $1.00 + $.25 per page