1. An error-correction method for use in decoding Reed-Solomon code that corrects errors in data by use of known error locations, whereby respective error symbols are corrected by use of n error vectors obtained by a series of steps comprising: (A) performing product sum arithmetic operations of syndromes S.nu.(.nu.=0 to n-1) and error locations X.sub.j (j=1 to n) on the basis of: EQU S.nu..sub.,i =S.nu..sub.,i-1 X.sub.i +S.nu..sub.+1,i-1 ( 1.ltoreq.i.ltoreq.n-1: n is the number of error symbols) where, (S.nu..sub.,0 =S.nu.) for sequentially obtaining an i.sup.th answer S.nu..sub.,i, and for finally obtaining S.sub.0,n-1 ; and (B) obtaining error vectors Y.sub.n by performing the following arithmetic operation by use of said S.sub.O,n-1, ##EQU23##