diff --git a/ChangeLog b/ChangeLog
index e22fdeea2..0407b6ac7 100644
--- a/ChangeLog
+++ b/ChangeLog
@@ -56,6 +56,9 @@ Bugfix
      generated in Visual Studio 2015. Reported by Steve Valliere. #742
    * Fix a resource leak in ssl_cookie, when using MBEDTLS_THREADING_C.
      Raised and fix suggested by Alan Gillingham in the mbed TLS forum. #771
+   * Fix 1 byte buffer overflow in mbedtls_mpi_write_string() when the MPI
+     number to write in hexadecimal is negative and requires an odd number of
+     digits. Found and fixed by Guido Vranken.
 
 = mbed TLS 2.4.1 branch released 2016-12-13
 
diff --git a/library/bignum.c b/library/bignum.c
index 4c99e04d6..8b9082cdc 100644
--- a/library/bignum.c
+++ b/library/bignum.c
@@ -534,7 +534,12 @@ int mbedtls_mpi_write_string( const mbedtls_mpi *X, int radix,
     n = mbedtls_mpi_bitlen( X );
     if( radix >=  4 ) n >>= 1;
     if( radix >= 16 ) n >>= 1;
-    n += 3;
+    /*
+     * Round up the buffer length to an even value to ensure that there is
+     * enough room for hexadecimal values that can be represented in an odd
+     * number of digits.
+     */
+    n += 3 + ( ( n + 1 ) & 1 );
 
     if( buflen < n )
     {
diff --git a/tests/suites/test_suite_mpi.data b/tests/suites/test_suite_mpi.data
index fa65b5f2a..da830feb8 100644
--- a/tests/suites/test_suite_mpi.data
+++ b/tests/suites/test_suite_mpi.data
@@ -46,6 +46,9 @@ mpi_read_write_string:16:"":16:"00":4:0:0
 Test mpi_read_write_string #9 (Empty MPI -> dec)
 mpi_read_write_string:16:"":10:"0":4:0:0
 
+Test mpi_write_string #10 (Negative hex with odd number of digits)
+mpi_read_write_string:16:"-1":16:"":3:0:MBEDTLS_ERR_MPI_BUFFER_TOO_SMALL
+
 Base test mbedtls_mpi_read_binary #1
 mbedtls_mpi_read_binary:"0941379d00fed1491fe15df284dfde4a142f68aa8d412023195cee66883e6290ffe703f4ea5963bf212713cee46b107c09182b5edcd955adac418bf4918e2889af48e1099d513830cec85c26ac1e158b52620e33ba8692f893efbb2f958b4424":10:"56125680981752282334141896320372489490613963693556392520816017892111350604111697682705498319512049040516698827829292076808006940873974979584527073481012636016353913462376755556720019831187364993587901952757307830896531678727717924"