diff --git a/NEWS.md b/NEWS.md
index 7251bace79..dc66ce2897 100644
--- a/NEWS.md
+++ b/NEWS.md
@@ -109,6 +109,8 @@ unit = "s")
 
 4. `fifelse` and `fcase` notify users that S4 objects (except `nanotime`) are not supported [#4135](https://github.com/Rdatatable/data.table/issues/4135). Thanks to @torema-ed for bringing it to our attention and Morgan Jacob for the PR.
 
+5. `frank(..., ties.method="random", na.last=NA)` now returns the same random ordering that `base::rank` does, [#4243](https://github.com/Rdatatable/data.table/pull/4243).
+
 
 # data.table [v1.12.8](https://github.com/Rdatatable/data.table/milestone/15?closed=1)  (09 Dec 2019)
 
diff --git a/R/frank.R b/R/frank.R
index 05fd7df754..763b8267e5 100644
--- a/R/frank.R
+++ b/R/frank.R
@@ -32,11 +32,14 @@ frankv = function(x, cols=seq_along(x), order=1L, na.last=TRUE, ties.method=c("a
     nas  = x[[ncol(x)]]
   }
   if (ties.method == "random") {
-    v = stats::runif(nrow(x))
     if (is.na(na.last)) {
       idx = which_(nas, FALSE)
-      set(x, idx, '..stats_runif..', v[idx])
-    } else set(x, NULL, '..stats_runif..', v)
+      n = length(idx)  # changed in #4243 to match base R to pass test 1369
+    } else {
+      idx = NULL
+      n = nrow(x)
+    }
+    set(x, idx, '..stats_runif..', stats::runif(n))
     order = if (length(order) == 1L) c(rep(order, length(cols)), 1L) else c(order, 1L)
     cols = c(cols, ncol(x))
   }
diff --git a/inst/tests/tests.Rraw b/inst/tests/tests.Rraw
index 2a42adf7a2..b1c080c393 100644
--- a/inst/tests/tests.Rraw
+++ b/inst/tests/tests.Rraw
@@ -5480,7 +5480,8 @@ test_no = 1368.0
 for (i in seq_along(dt)) {
   col = dt[[i]]
   for (j in list(TRUE, FALSE, "keep")) {
-    for (k in c("average", "min", "max", "first", "last")) {
+    # ensure consistency with base::rank ties.methods as advertised
+    for (k in eval(formals(base::rank)$ties.method)) {
       if (k == "random") set.seed(45L)
       if (class(col) == "integer64") {
         r1 = rank(as.integer(col), ties.method=k, na.last=j)
@@ -5511,7 +5512,8 @@ if (test_bit64) dt[, DD := as.integer64(DD)]
 test_no = 1369.0
 for (i in seq_along(dt)) {
   col = dt[[i]]
-  for (k in c("average", "min", "max", "first", "last")) {
+  # ensure consistency with base::rank ties.methods as advertised
+  for (k in eval(formals(base::rank)$ties.method)) {  # 'random' on now with tweak to match base in #4243
     if (k == "random") set.seed(45L)
     if (class(col) == "integer64") {
       r1 = rank(as.integer(col), ties.method=k, na.last=NA)