The invention has for its object to provide a preparation method for preparing an anion-exchangeable LDH by decarbonation of a carbonate ion type LDH, which makes sure de carbonation is implemented with safety in a continuous manner while crystal shape, crystal structure and crystallinity are kept intact. The invention provides a preparation method for preparing an anion-exchangeable, layered double hydroxide wherein a carbonate ion type layered double hydroxide (LDH) having a composition represented by a general formula: Q x R(OH) z (CO 3 2- ) 0.5-y/2 (X - ) y ·nH 2 O where x is indicative of a numeral range of 1.8‰¦x‰¦4.2; z is indicative of 2(x+1); y is indicative of a minimum value of at least 0 that increases to less than 1 when anions (X - ) remain or a part of anions is introduced; Q is a divalent metal ion; R is a trivalent metal ion; and n is 2 ±2 is used as a starting material, and y in said general formula increases to a maximum of 1 by substitution of a minus monovalent anion (X -1 ) at
